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Introduction to simple machines - class-X

Description: introduction to simple machines
Number of Questions: 86
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Tags: lever machines simple machines common machines physics simple machine
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Graphite powder is used in machines to_______

  1. enhance friction

  2. enhance profit

  3. reduce friction

  4. reduce efficient


Correct Option: C
Explanation:

Graphite powder is used in some machines to reduce friction. Ball bearing coverts sliding friction into rolling friction.

When the height of the inclined plane decreases :

  1. The mechanical advantage decreases

  2. The mechanical advantage increases

  3. Effort increases

  4. It will not have any effect on the mechanical advantage


Correct Option: B
Explanation:

The mechanical advantage increases with decrease in height of inclined plane.

When the height of the inclined plane decreases :

  1. the mechanical advantage decreases

  2. the mechanical advantage increases

  3. effort increases

  4. it will not have any effect on the mechanical advantage


Correct Option: B

For an ideal machine:

  1. Output= input

  2. Output> input

  3. Output< input

  4. Output ${\geq}$ input


Correct Option: A
Explanation:

In an ideal machine there will be zero energy loss hence output will be equal to input

Mechanical advantage of a lever is

  1. load + effort

  2. load $\times$ effort

  3. $ \dfrac{load}{effort}$

  4. $ \dfrac{effort}{load}$


Correct Option: D

Wedge is a :

  1. First order lever

  2. Wheel and-axle

  3. Inclined plane

  4. None of the above


Correct Option: C

Efficiency of machine is

  1. Ratio of velocity of effort to velocity of load

  2. Ratio of the load to its effort

  3. Ratio of useful work done by the machine to the work put to the machine by its effort

  4. All


Correct Option: C
Explanation:

Mechanical advantage (MA) is the ratio of the load to its effort.
efficiency of machine (n) = MA/VR
Velocity Ratio (VR) is the ratio of the velocity of effort to velocity of load.

Relationship between the mechanical advantage and velocity ratio of an ideal machine is

  1. Velocity Ratio < mechanical advantage

  2. Velocity Ratio = Mechanical advantage

  3. Velocity ratio > Mechanical advantage

  4. All


Correct Option: B
Explanation:

For ideal machine, efficiency = 1

effeciency = Mechanical advantage/ velocity ratio
So, for ideal machine, Mechanical advantage = velocity ratio

Relationship between mechanical advantage and velocity ratio for a practical machine is

  1. Velocity ratio = Mechanical advantage

  2. Velocity ratio > Mechanical advantage

  3. Velocity ratio < mechanical advantage

  4. All


Correct Option: B
Explanation:

For a practical machine, velocity ratio is greater than mechanical advantage
V.R > M.A.

The ratio of the load to the effort is called.

  1. Mechanical advantage

  2. Velocity ratio

  3. Efficiency of machine

  4. None


Correct Option: A
Explanation:

Ratio of load to the effort is k/a mechanical advantage of the machine. The ratio of the velocity of effort to its velocity of the load is called its velocity ratio of machine.

Ratio of velocity of effort to the velocity of load is called.

  1. Mechanical advantage

  2. Velocity ratio

  3. Efficiency of machine

  4. None


Correct Option: B
Explanation:

Ratio of the velocity of effort to the velocity of load is called velocity ratio of machine. Ratio of the load to its effort is called mechanical advantage of machine.

It is difficult to climb the steps having greater inclination. Why?

  1. Less erect steps require less energy

  2. Greater inclination requires less effort because of the high mechanical advantage

  3. Greater inclination requires more effort because of the low mechanical advantage

  4. None of the above


Correct Option: C

Velocity Ratio of a machine is more than 1. It 

  1. Acts as a force multiplier

  2. Gives loss of speed

  3. A and B

  4. Either A or B


Correct Option: C
Explanation:

VR = Velocity of effort / velocity of load

VR > 1 means velocity of effort is more than load, hence loss of speed
VR > 1 then machine acts as a force multiplier

A force of 10N raised a load of 400 kg. Calculate mechanical advantage of the machine.

  1. 50

  2. 400

  3. 10

  4. 4000


Correct Option: B
Explanation:

Mass given $= 400\  kg$


Effort $= 10\ N$

$MA = \dfrac{load}{effort} = \dfrac{4000}{10} = 400$.

A machine is used to displace a load of $200$ N through $5$ cm by an effort of $10$ N. If efficiency of the machine is $50\%$. Find its mechanical equivalent.

  1. 5

  2. 20

  3. 10

  4. 2


Correct Option: B
Explanation:

Load = $w = 200N$
Distance moved by the load = $5cm = .05m$
$Effort (P) = 10N$
$n(Efficiency) = 50\%$
$MA = Load/Effort = W/P=200N/10N=20$

A pulley system of VR of 2 and efficiency of 50%. If the effort moves through a distance of 5m. Calculate the distance moved by the load.

  1. 2m

  2. 5.6m

  3. 10m

  4. 2.5m


Correct Option: D
Explanation:

Given:  $VR=2$


From the relation $VR=\dfrac{\text{Distance moved by effort}}{\text{distance moved by load}}$


Using formula we get distance moved by the load is $2.5m$

........ is defined as the ratio of the distance moved by effort and load, in the same time interval.

  1. Velocity ratio

  2. Mechanical advantage

  3. Both

  4. None


Correct Option: A
Explanation:

Velocity ratio = $\displaystyle \frac { Distance\quad moved\quad by\quad the\quad effort }{ Corresponding\quad distane\quad moved\quad by\quad the\quad load } $
It only depends on the design of machine and is always same for a particular machine.

Efficiency is

  1. $\displaystyle \frac { Energy\quad input }{ Energy\quad output } \times 100$

  2. $\displaystyle \frac { mechanical\quad advantage }{ velocity\quad ratio } \times 100$

  3. Both

  4. None


Correct Option: C
Explanation:

As no machine is perfectly efficient.
So, we define efficiency as efficiency = $\displaystyle \frac { Energy\quad input }{ Energy\quad output } \times 100$
Also Efficiency = $\displaystyle \frac { mechanical\quad advantage }{ velocity\quad ratio } \times 100$
A petrol engine is about 30% efficient, a diesel engine is 40% efficient.

A machine in which displacement of load is more than the displacement of effort, will have the velocity ratio

  1. More than 1

  2. Less than 1

  3. Equal to 1

  4. All


Correct Option: B
Explanation:

A machine in which displacement of load is more than the displacement of effort, will have the velocity ratio more than 1.

Friction has no effect on 

  1. Velocity Ratio

  2. Mechanical Advantage

  3. Efficiency

  4. All of the above


Correct Option: A
Explanation:

Friction has effect on Mechanical Advantage and efficiency but not Voltage Ratio.

Effeciency of inclined plane

  1. Zero

  2. One

  3. Two

  4. Three


Correct Option: B
Explanation:

$\eta=\frac{M.A}{V.R}=\frac{l}{h(l/h)}=1$
$M.A=\frac{l}{h}, V.R=\frac{l}{h}$

Mechanical advantage of an inclined plane is 

  1. Always smaller than $1$

  2. Always greater than $1$

  3. Always equal to $1$

  4. All


Correct Option: B
Explanation:

An inclined plane is a sloping surface that behaves like a simple machine whose mechanical advantage is always greater than $1$.

Akhil has to lift a load of $800N$ onto a platform of $2m$ height. Instead, he pushes the load up a ramp $4m$ long. Find the force required to lift the load vertically up.

  1. $200N$

  2. $600N$

  3. $400N$

  4. $800N$


Correct Option: D
Explanation:

The vertical force is the gravitational force means weight of the load. 

According to question, the weight of load is $mg=800 N$, this will be the required force to lift the load vertically.  

Mechanical advantage =________.

  1. Load $-$ effort

  2. Load $\times $ effrot

  3. Load $/$ effort

  4. None of the above


Correct Option: C

Which of the following statements is NOT correct?

  1. In a first order lever, the fulcrum is placed between the effort and the load

  2. The mechanical advantage of a second class levers is greater than $1$ as load is situated in between to effort and fulcrum.

  3. An inclined plane in a hospital, helps pushing a wheel chair easily.

  4. A crow bar is an example of second class lever


Correct Option: D

Mechanical advantage of wheel and axle is: ($R=$ radius of the wheel, $r$ = radius of the axle)

  1. $R+r$

  2. $R/r$

  3. $r/R$

  4. $R-r$


Correct Option: B
Explanation:

Mechanical advantage is the amplification in force due to the use of a machine . The mechanical advantage of wheel and axle is given by 

                  $M.A.=R/r$

The ratio of the work output to the work input of a machine is

  1. mechanical advantage

  2. efficiency

  3. work

  4. power


Correct Option: B
Explanation:

Efficiency is the (often measurable) ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without waste. In more mathematical or scientific terms, it is a measure of the extent to which input is well used for an intended task or function (output).

Which of the following is not considered a simple machine?

  1. Wedge

  2. Pulley

  3. Lever

  4. Wheelbarrow


Correct Option: D
Explanation:

A wheelbarrow is example 3 class third lever rest all are example of simple machine. hence option D is incorrect

A screwdriver can be used to open a can of paint. In this situation, the screwdriver is being used as a

  1. wheel and axle

  2. screw

  3. lever

  4. inclined plane.


Correct Option: C
Explanation:

C lever. The edge of the can serves as the fulcrum and the lid is the load.

The ratio of distance travelled by the effort to the distance travelled by the load in the machine is called-

  1. velocity ratio

  2. distance ratio

  3. work ratio

  4. none of these


Correct Option: A
Explanation:

The velocity ratio is define as $VR=\dfrac{{Effort}{} _{distance}}{{load}{} _{distance}}$
hence option A is correct.

An oar is used to row a boat. The distance between the oar lock (fulcrum) and the rower's hand is $104 cm$. This distance is considered

  1. the effort distance

  2. the resistance distance.

  3. the mechanical advantage of the oar

  4. the effort force


Correct Option: A
Explanation:

the distance between fulcrum and effort is called effort distance.
Option A is correct

The mechanical advantage of each machine is determined by

  1. adding the mechanical advantage for each simple machine

  2. finding the simple machine with the largest mechanical advantage

  3. finding the average mechanical advantage for the simple machines

  4. multiplying the mechanical advantage for each simple machine


Correct Option: D
Explanation:

The mechanical advantage of each machine is determined by  multiplying the mechanical advantage for each simple machine.
Option D is correct

The mechanical advantage of another oar is $3.00$. If the resistance force of the water is $35.0\ lb$, what is the effort force exerted by the rower?

  1. 11.7 lb

  2. 0.0857 lb

  3. 105 lb

  4. 32.0 lb


Correct Option: A
Explanation:

The $effort=\dfrac{MA}{load}=\dfrac{35lb}{3}=11.7lb$

In a lifting machine, an effort of $500$ N is to be moved by a distance of $20$ m to raise a load of $10000$ N by a distance of $0.8$ m. Determine the velocity ratio and mechanical advantage?

  1. 10 and 35

  2. 20 and 35

  3. 10 and 25

  4. 25 and 20


Correct Option: D
Explanation:
Distance moved by effort is 20m,that of load is 0.8m

$VR=\dfrac{{E}{} _{d}}{{L}{} _{d}}$

$VR=\dfrac{20}{0.8}$

$VR=25$

the load is 10,000N and effort=500N

$MA=\dfrac{{load}{} _{d}}{{effort}{} _{d}}$

$MA=\dfrac{10000}{500}$

$MA=20$

In an ideal machine,

  1. Velocity Ratio > Mechanical Advantage

  2. Velocity Ratio =0.5 X Mechanical Advantage

  3. Velocity Ratio < Mechanical Advantage

  4. Velocity Ratio = Mechanical Advantage


Correct Option: D
Explanation:

For an ideal machine the Velocity ratio is always equal to Machanical advantage.

$VR=MA$

Hence option D is correct

What load will be lifted by an effort of $12$ $N$ if the velocity ratio is $18$ and the efficiency of the machine at this load is 60%?

  1. 1N

  2. .130N

  3. 1.30N

  4. 13N


Correct Option: B
Explanation:

$\eta=\dfrac{load}{effort*VR}*100$

$load=\eta*effort*VR=0.6*12*18=130N$

In a lifting machine, the efforts required for lifting loads of $20$ N and $30$ N were $5$ N and $6$ N respectively. If the velocity ratio of the machine is $20$, determine efficiencies corresponding to loads of $20 $ N and $30$ N

  1. 25 % and 20%

  2. 35% and 55%

  3. 30% and 50%

  4. 60% and 65%


Correct Option: A
Explanation:

Let us take first case,


 in which $load=20N , effort =5N ,VR=20$

$Efficiency=\dfrac{load}{VR*effort}*100$

Putting above values, we get

$Efficiency=\dfrac{20}{20*5}*100=20%$

In second case we have.  $load=30N , efoort =6N ,VR=20$

$Efficiency=\dfrac{load}{VR*effort}*100$

Putting values we get,

$Efficiency=\dfrac{30}{20*6}*100=25%$

Hence$ Efficiency=25%,20%$

The mechanical advantage for a pulley system is determined by

  1. counting the number of strands holding the resistance force.

  2. counting the number of strands holding and not holding the resistance force.

  3. adding the radii of the pulleys.

  4. multiplying the radii of the pulleys.


Correct Option: B

If a machine overcomes a load $L$ and the distance travelled by the load is $L _d$. Similarly, the effort applied in the machine is $E$ and the distance travelled by effort is $E _d$, and $'T'$ is the time taken then velocity ratio can be written as 

  1. $\dfrac{E _d}{L _d}$

  2. $\dfrac{L _d}{E _d}$

  3. $\dfrac{E _d}{\sqrt{L _d}}$

  4. $\dfrac{\sqrt{L _d}}{E _d}$


Correct Option: A
Explanation:

The VR is define as ratio of distance travelled by effort:distance travelled by load


$VR=\dfrac{{E}{} _{d}}{{L}{} _{d}}$

option A is correct.

In a lifting machine, an effort of 500 N is to be moved by a distance of 20 m to raise a load of 10,000 N by a distance of 0.8 m. Determine the velocity ratio and mechanical advantage.

  1. 25 and 20

  2. 23 and 22

  3. 20 and 30

  4. 25 and 35


Correct Option: A
Explanation:
Distance moved by effort is 20m,that of load is 0.8m

$VR=\dfrac{{E}{} _{d}}{{L}{} _{d}}$

$VR=\dfrac{20}{0.8}$

$VR=25$

the load is 10,000N and effort=500N

$MA=\dfrac{{load}{} _{d}}{{effort}{} _{d}}$

$MA=\dfrac{10000}{500}$

$MA=20$

Fill in the blank.
In second order lever, velocity ratio 

  1. is greater than one

  2. is less than one

  3. it may be greater than one or less than one

  4. none of the above


Correct Option: A
Explanation:

The VR of second order lever is always grater than 1 because effort arm is always longer than load arm.


$VR=\dfrac{{E}{} _{d}}{{L}{} _{d}},Vr>1$


In a lifting machine, an effort of 500 N is to be moved by a distance of 20 m to raise a load of 10,000 N by a distance of 0.8 m. Determine the effort lost in friction

  1. 100 N

  2. 120 N

  3. 80 N

  4. 0 N


Correct Option: A

Efficiency of a machine can also be written as 

  1. $\dfrac{\text{velocity ratio}}{\text{mechanical advantage}} \times 100 $ %

  2. $\dfrac{\text{mechanical advantage}}{\text{velocity ratio}} \times 100 $ %

  3. $\dfrac{\text{mechanical advantage}}{\text{velocity of the gear}} \times 100 $ %

  4. None of the above


Correct Option: B
Explanation:

$effiency=\eta=\dfrac{Machanical-advantage}{velocity-ratio}*100$

Fill in the blank.
In the first order of lever, velocity ratio is usually __than 1 but could be __ or equal to 1

  1. greater, less

  2. less, more

  3. greater, more

  4. less, less


Correct Option: A

You do 1200 J of work with gears. If the gears do 1000 J of work, what is the efficiency of the gears?

  1. $93.33$ %

  2. $73.33$ %

  3. $83.33$ %

  4. $80.33$ %


Correct Option: C
Explanation:

$\eta=\dfrac{Load}{effort}*100=\dfrac{1000}{1200}*100=83.33\%$

You do 1260 J of work with a wheel and axle. If the wheel and axle does 1200 J of work, what is the efficiency of the wheel and axle?

  1. More than 95 %

  2. Equal to 95 %

  3. Less than 95 %

  4. Less than 83.33 %


Correct Option: A
Explanation:

$\eta=\dfrac{Load}{effort}*100=\dfrac{1200}{1260}*100=95.23\%$

It is easier to draw up a wooden block along an inclined plane than to haul it vertically, principally because:

  1. the friction is reduced

  2. the mass becomes smaller

  3. only a part of the weight has to be overcome

  4. $g$ becomes smaller


Correct Option: C
Explanation:

The vertical plane $W=mgh$
for inclined plane $W'=mghsin(Q)$
$sinQ<1$
$W>W'$
hence only one part of weight is to overcome

A pump ejects $12000\ kg$ of water at the speed of $4\ { m }/{ s }$ in $40\ second.$ Find the average rate at which the pump is working

  1. $2.4kw$

  2. $2.5kw$

  3. $2.3kw$

  4. $1.7kw$


Correct Option: A
Explanation:
$F=ma=12000\times \dfrac {4}{40}=1200\ N$
$A=F/m=1200/1200=1/10\ m/s^2$
$s=ut +\dfrac {1}{2}at^2=0+\dfrac {1}{2}\times \dfrac {1}{10}\times 40\times 40=80\ m$
then, $W=Fs=80\times 1200=96000\ J$
rate of working, $P=\dfrac {W}{t}$
$P=\dfrac {96000}{40}=2400W=2.4\ kW$

The mechanical advantage of inclined plane of angle of inclination $60^{\circ}$ is equal to :

  1. $\dfrac{2}{\sqrt{3}}$

  2. $cosec 30^o$

  3. both (1) and (2)

  4. none of the above


Correct Option: A
Explanation:

Mechanical advantage of an inclined plane at an angle $\theta$ is  $ \dfrac{Length }{height}$$ = \dfrac{l}{h} = \dfrac{1}{sin \theta}$


$ = cosec \theta = cosec 60^o = \dfrac{1}{sin 60^o} = \dfrac{2}{\sqrt{3}}$

Mechanical advantage is equal to 

  1. $2 \pi R \times 2 \pi r$

  2. $ 2 \pi R - 2 \pi r$

  3. $\displaystyle \frac{2\pi R}{2 \pi r}$

  4. None of these


Correct Option: C

Akhil has to lift a load of 800 N onto a platform of 2 m height. Instead, he pushes the load up a ramp 4 m long. Find the force required to roll the load up the ramp.

  1. 200 N

  2. 600 N

  3. 400 N

  4. 800 N


Correct Option: C
Explanation:

Force required to roll the load up the ramp (F) $=\displaystyle \frac{load \times height}{distance}$
$= 800 \displaystyle \times \frac{2}{4} = 400 N$

The ratio of the radius of two wheels A and B are in the ratio 3 : 7 respectively and the ratio of their respective axles is 5 : 4. Identify the wheel and axle that has greater mechanical advantage?

  1. A

  2. B

  3. Both have same

  4. Can't say


Correct Option: B
Explanation:

The mechanical advantage of a wheel and axle $= \displaystyle \frac{Radius \ of \ wheel}{Radius \ of \ the \ axle}$
$MA _A = \displaystyle \frac{R _1}{r _1} $ and  $MA _B = \displaystyle \frac{R _2}{r _2}$
Given $ r _1  :  r _2  = 5 : 4$
$R _1  :  R _2  = 3  :  7$
$ \displaystyle \frac{MA _A}{MA _B} = \frac{R _1}{r _1} \times \frac{r _2}{R _2}$
$\displaystyle = \frac{3}{5} \times \frac{4}{7} = \frac{12}{35}$
$MA _B >  MA _A$

In a wheel-axle arrangement, the radius of wheel is 25 times more than the radius of an axle. Find the mechanical advantage of the machine.

  1. 20

  2. 25

  3. 30

  4. 35


Correct Option: B
Explanation:

The mechanical advantage of a wheel and axle $= \displaystyle \frac{Radius  of  wheel}{Radius  of  the  axle}$
Given radius of wheel $=$ 25 $\times$ radius of axle
$MA = \displaystyle \frac{25 \times radius  of  axle}{radius  of  axle} = 25$

Which of the following statements in NOT correct?

  1. In a first order lever, the fulcrum is placed between the effort and the load.

  2. The mechanical advantage of a second class levers is greater than 1 as load is situated in between to effort and fulcrum.

  3. An inclined plane in a hospital, helps in pushing a wheel chair easily.

  4. A crow bar is an example of second class level.


Correct Option: A,B,C

An effort of 20 kgf is applied on a machine through a distance of 80 cm, when a load of 30 kgf moves through a distance of 1 cm. Calculate the velocity ratio of the machine.

  1. 40

  2. 80

  3. 160

  4. 60


Correct Option: B
Explanation:

Velocity ratio $= \displaystyle \frac{distance \ of \ the \ effort}{distance \ moved \ by \ the \ load}$
$= \displaystyle \frac{80  cm}{1  cm}= 80$

Akhil has to lift a load of 800 N onto a platform of 2 m height. Instead, he pushes the load up a ramp 4 m long. Find the work done by Akhil in lifting the load vertically up.

  1. 800 J

  2. 1600 J

  3. 400 J

  4. 200 J


Correct Option: B
Explanation:

The work done by Akhil in lifting the load vertically up $=$ Force $\times$ height
$= 800 \times 2 = 1600 \ J$

A crow-bar of length $2.0$ m is used as a machine to lift a box of $100$ kgf by placing a fulcrum at a distance of $0.1$ m from the box. Calculate the effort required.

  1. 1.9 m

  2. 19 m

  3. 29 m

  4. 30 m


Correct Option: A

A nut can be opened by a lever of length $0.25$ m by applying a force of $80$ N. What should be the length of the lever if a force of $32$ N is enough to open the nut?

  1. $625$ m

  2. $1625$ m

  3. $0.625$ m

  4. $6.25$ m


Correct Option: C

A rubber ball dropped from a height of $20\ m (g = 10\ m/s^{2})$ falls on the roof of an elevator going up at $2\ m/s$. If the collision of the ball with the elevator is elastic, the ball rebounds with a velocity of

  1. $20\ m/s$

  2. $22\ m/s$

  3. $24\ m/s$

  4. $26\ m/s$


Correct Option: C

Efficiency of engine is $\eta _1$ at $T _1 = 200^\circ C$ and $T _2 = 0^\circ C$ and $\eta _2$ at $T _1 = 0^\circ C$ and $T _2 = -200 K$. Find the ratio of $\dfrac{\eta _1}{\eta _2}$.

  1. $1.00$

  2. $0.577$

  3. $0.721$

  4. $0.34$


Correct Option: C

A man of mass $80kg$ carrying a load of $20kg$ walks up a stair case in $20s$. If the number of steps is $40$ and width and height of each step are $20cm$ and $15cm$ respectively. The efficiency of the man is

  1. $20 \%$

  2. $25\%$

  3. $40\%$

  4. $50\%$


Correct Option: A

A man uses a crowbar of length $1.5m$ to raise a load of $75kgf$ by putting a sharp edge below the bar at a distance $1m$ from his hand. Calculate the mechanical advantage. 

  1. $0$

  2. $1$

  3. $2$

  4. $4$


Correct Option: C
Explanation:

Load $ = 75 kgf$
Length of crowbar $= 1.5 m$
Effort arm $= 1 m $
So, Load Arm $= \text{Length of crowbar - Effort arm}$


$\Rightarrow 1.5 - 1 = 0.5 m$
Mechanical Advantage $= \dfrac{\text{Effort Arm}}{\text{Load Arm}} = \dfrac{1}{0.5} =2$

A water -pump driven by petrol raises water at a rate $ 0.5 m^3/min $ from a depth of 30 m. if the pump is 70% efficient, what power is developed by the engine?

  1. 1750W

  2. 2450W

  3. 3500W

  4. 7000W


Correct Option: C

A $20\ N$ metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads $40\ N$. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now reads $16\ N$. The reading of the weighing machine will be 

  1. $36\ N$

  2. $60\ N$

  3. $44\ N$

  4. $56\ N$


Correct Option: C

A man uses a crowbar of length $1.5m$ to raise a load of $75kgf$ by putting a sharp edge below the bar at a distance $1m$ from his hand. Calculate the effort needed.

  1. $75kgf$

  2. $375kgf$

  3. $37.5 gf$

  4. $37.5kgf$


Correct Option: D
Explanation:

Load $ = 75 kgf$
Length of crowbar $= 1.5 m$
Effort arm $= 1 m $
So, Load Arm $= \text{Length of crowbar - Effort arm}$
$\Rightarrow 1.5 - 1 = 0.5 m$
Mechanical Advantage $= \dfrac{\text{Effort Arm}}{\text{Load Arm}} = \dfrac{1}{0.5} =2$


Effort needed $= \dfrac{\text{Load}}{\text{Mechanical Advantage}} = \dfrac{75}{2} = 37.5 kgf$

A boy can exert a maximum effort of $250\  N$, so he uses an inclined plane to lift the load up. What should be the minimum length of the plank used by him to lift a mass of $ 50 \ kg$ to a height of $1 \ m$ ?

  1. $2$ $ m $

  2. $5$ $ m $

  3. $25$ $ m$

  4. $6$ $ m$


Correct Option: A
Explanation:

Work done  $W = mgh$
$W = 50\times 10\times 1$  $N$
$W=500 N $
$W =$ Effort $\times$ distance
Distance$=500/250= 2m$

A coolie uses a sloping wooden plank of length $2.0 m$ to push up a drum of mass $100 kg$ into the truck at a height $1.0 m$. What is the mechanical advantage of the sloping plank ?

  1. 6

  2. 5

  3. 2

  4. 10


Correct Option: C
Explanation:

Length of the sloping wooden plank , $l = 2 m$
Vertical height , $h = 1 m$
We, know that for a inclined plane,
Mechanical Advantage $= \dfrac{Length \ of \ the \ incline}{vertical \ height}$
$\Rightarrow \dfrac{l}{h} = \dfrac{2}{1} = 2$

A fire tongs has its arms $20cm$ long. It is used to lift a coal of weight $1.5kgf$ by applying an effort at a distance $15cm$ from the fulcrum. Find the mechanical advantage of fire tongs.

  1. $3$

  2. $0.50$

  3. $0.90$

  4. $0.65$


Correct Option: A
Explanation:

Effort Arm $ = 15 cm$
Load Arm $ = 20 - 15 = 5 cm$
Mechanical Advantage $= \dfrac{\text{Effort Arm}}{\text{Load Arm}} = \dfrac{15}{5} = 3$

A fire tongs has its arms $20 \ cm$ long. It is used to lift a coal of weight $1.5 \ kgf$ by applying an effort at a distance $15 \ cm$ from the fulcrum. Find the effort needed.

  1. $0.2 kgf$

  2. $1.5 kgf$

  3. $2.5 kgf$

  4. $2.0 kgf$


Correct Option: D
Explanation:

$Load= 1.5kgf$
$Load \ arm= 20cm$
$Effort \ arm=15 cm$
$Effort \ = 20 \times 1.5/15= 2.0kgf$
The fulcrum in tongs is the joint end of the arms

It is harder to cut an apple with a butter-knife, because:

  1. butter-knife has more inclination

  2. mechanical advantage of a butter-knife is less

  3. it has a high angle of wedge

  4. all the above


Correct Option: D

It is difficult to climb the steps having greater inclination. Why?

  1. Less erect steps require less energy

  2. Greater inclination requires less effort because of the high mechanical advantage

  3. Greater iriclination requires more effort because of the low mechanical advantage

  4. None of the above


Correct Option: C

For a _________, the mechanical advantage is always less than one.

  1. first order lever

  2. second order lever

  3. third order lever

  4. both A and C


Correct Option: C

Mechanical advantage of a second order lever is :

  1. always less than one

  2. less than or equal to one

  3. always greater than one

  4. greater than or equal to one


Correct Option: C

If the threads of a screw are closer : 

  1. Mechanical advantage decreases

  2. Inclination increases

  3. Effort required will be less

  4. All of the above


Correct Option: D

The force applied on the machine to overcome the load is called

  1. Mechanical advantage

  2. Load

  3. Effort

  4. All of the above 


Correct Option: C
Explanation:

Definition of effort $\left( \varepsilon \right)$. The resistive or opposing force to be overcome by a machine is called the load $\left(L\right)$.

The resistive or opposing force to be overcome by a machine is called the

  1. Load

  2. Effort

  3. Mechanical advantage

  4. All


Correct Option: A
Explanation:

Definition of load. The force applied on the machine to overcome the load is called effort $\left(\varepsilon \right)$.

When the same amount of force is applied :

  1. A nail travels more distance than a screw into the wood board

  2. Screw travels more distance than the nail

  3. Both pierce the wood board to equal distance

  4. None of the above


Correct Option: B

A boy can exert a maximum force of $10$kg, i.e he cannot lift vertically a load of mass more than $10$kg. Now if he wants to raise a load of mass $20$kg on to a high eall, he can do it with the help of an inclined place making an angle $\theta$ with the horizontal. Find $\theta$.

  1. $60^o$

  2. $80^o$

  3. $30^o$

  4. $20^o$


Correct Option: C
Explanation:

$sin \theta=\dfrac{1}{M.A}=\dfrac{Effort}{Load}=\dfrac{10}{20}=\dfrac{1}{2}$
Thus, by placing a wooden plank at $\theta=30^o$ an angle equal to $30^o$ with the horizontal group can push the load of mass $20$Kg at any height by exerting a force(or effort) of $10$kg.

The velocity ratio of a machine is 1 if 

  1. The displacement of load is equal to the displacement of effort

  2. The displacement of load > equal to the displacement of effort

  3. The displacement of load < equal to the displacement of effort

  4. None of the above 


Correct Option: A
Explanation:

The velocity ratio of a machine is equal to the displacement of effort such a machine changes the direction of effort.

As the closeness of threading increases in a screw :

  1. mechanical advantage decreases

  2. effort required will be less

  3. inclination increases

  4. all the above


Correct Option: B

It is harder to cut an apple with a butter knife, because :

  1. Butter knife has more inclination

  2. Mechanical advantage of butter knife is less

  3. It has a high angle of wedge

  4. All of the above


Correct Option: D

If a machine overcomes a load $L$ and the distance travelled by the load is $25 m$. Similarly, the effort applied in the machine is $E$ and the distance travelled by effort is $75 m$, and $'T'$ is the time taken,then velocity ratio is:

  1. $\dfrac{1}{3}$

  2. $\dfrac{2}{3}$

  3. $\dfrac{3}{1}$

  4. $1$


Correct Option: A
Explanation:
The VR is define as ratio of distance travelled by effort:distance travelled by load

$VR=\dfrac{{E}{} _{d}}{{L}{} _{d}}$


$VR=\dfrac{25}{75}$

$VR=\dfrac{1}{3}$

option A is correct.

A load will be lifted by an effort of 12 N, the velocity ratio is 18 and the efficiency of the machine at this load is 60%, if the machine has a constant frictional resistance, determine the law of machine.

  1. P = W/18 + 4.8

  2. P = W/8 + 6.4

  3. P = W/14 + 8.2

  4. none of these


Correct Option: A

In a simple machine, whose velocity ratio is $30$, a load of $2400$ N is lifted by an effort of $150$ N and a load of $3000$ N is lifted by an effort of $180$ N. Find the law of machine -

  1. $P = 0.50W + 144$

  2. $P = 0.60W + 25$

  3. $P = 0.05 W + 144$

  4. $P = 0.05 W + 30$


Correct Option: D

In a simple machine, whose velocity ratio is $30$, a load of $2400 N$ is lifted by an effort of $150$ N and a load of $3000$ N is lifted by an effort of $180$ N. Calculate the amount of effort wasted in overcoming the friction using a force of $200 N$. 

  1. 86.67N

  2. 58.25N

  3. 89.25N

  4. 89.89N


Correct Option: A

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant, the gun fires 10 bullets/second, each of mass 10 g with a velocity of 500 m s$^{-1}$. The acceleration of the car is

  1. 0.025 ms$^{-2}$

  2. 0.25 ms$^{-2}$

  3. 0.5 ms$^{-2}$

  4. 500 ms$^{-2}$


Correct Option: A
Explanation:

$M _{car}=2000kg$


$n=10 \ bullets/s$

$M _{b}=10g=0.01kg$

$V _{b}=500m/s$

Momentum of each bullet $=0.01\times 500$

$(M _{b}V _{b})P _{b}=5kgm/s$

Force on car $=nP _{b}$

                       $50kgm/s^{2}$
$F _{car}=50N$

$a _{car}=\dfrac{50}{2000}=\dfrac{1}{40}$

$a _{car}=0.025m/s^{2}$

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