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The turning effect of a force - class-XII

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A couple produces motion in a straight line.

  1. True

  2. False


Correct Option: B
Explanation:

a couple produces rotational motion of a body . 

so the answer is B.

While opening a tap with two fingers, the forces applied are  

  1. equal in magnitude

  2. parallel to each other

  3. opposite in direction

  4. All of the above


Correct Option: D
Explanation:

While opening a tap with two fingers, a couple should be applied which is defined as a pair of parallel equal forces acting in opposite direction about two different axis.

On applying a constant torque on a body-

  1. linear velocity increases

  2. angular velocity changes

  3. it will rotate with constant angular velocity

  4. it will move with constant velocity


Correct Option: B

_____ is applied to unwind a screw.

  1. Single force

  2. Couple

  3. Parallel force

  4. None of these


Correct Option: B
Explanation:

Two equal and opposite forces are applied about different axis, which is termed as couple, to unwind a screw.

It becomes easier to open or close a door turning about its hinges if the force is applied at the:

  1. Two third of the door

  2. Free edge of the door

  3. Middle of the door

  4. Point near the hinges


Correct Option: B
Explanation:

Torque acting about any point O         $\tau _o = rF$                 for $sin\theta = 1$

where $r$ is the distance of the application of force from point O.
As  $r$ is maximum when a force is applied at the free end of the door, thus less amount of force is required to produce the same torque. Hence it is easier to open or close the door if force is applied at its free end. 

State whether true or false.
A spanner with a longer handle can tighten nuts and bolts with less effort.

  1. True

  2. False


Correct Option: A
Explanation:

We know, 

Moment of force = Force \times Distance between action point and force applied.
$\therefore T = F \times R$
As, R increases, T also increases.
So, we required to get less effort.

Which of the following playground equipment make use of the turning effect of forces?

  1. See-saw

  2. Slide

  3. Swing

  4. Toy horse


Correct Option: A,C,D
Explanation:

See-saw, Swing and Toy horse are the playground equipment make use of the turning effect of forces.

The spanner with a longer handle can tighten nuts and bolts with less effort.

  1. True

  2. False


Correct Option: A
Explanation:

spanner with longer handle needs less force to generate same torque than with spanner with short handle .

so the answer is A.

Self balancing toys have curved and heavy base area.

  1. True

  2. False


Correct Option: A
Explanation:

if the base area will be heavy than the centre of gravity will be near to ground and if the base area is curved than the object will come in its balanced position everytime due gravitational torque.

so the answer is A.

Which of the following sports uses the turning effect of forces?

  1. Cycling

  2. Swimming

  3. Badminton

  4. Hockey


Correct Option: A,B,C,D
Explanation:

cycling , swimming , badminton and hockey all these sports makes use of turning effect  of forces while play. 

so the answer is A,B,C and D .

For a rigit body, we know that if verious forces act at various points in it , the resultant motion is as if a net force acts on the CM(centre of mass)  causing translation and a net torque at the CM causing rotation around an axis through the CM. for the earth-sun system (approximating the earth as a uniform density sphere).

  1. the torque is zero

  2. the torque causes the earth to spin

  3. the rigid body result is not applicable since the earth is not ever approximately a rigid body

  4. the torque causes the earth to move around the sun


Correct Option: B

The angular momentum of body remains conserve if:

  1. applied force on body is zero

  2. applied torque on body is zero.

  3. applied force on body is constant

  4. applied torque on body is constant.


Correct Option: B
Explanation:

Just as linear momentum is conserved when there is no net external forces$,$

angular momentum is constant or conserved when the net torque is zero$.$
Hence,
option $(B)$ is correct answer.

A body is acted upon by two forces each of magnitude $F$, but in opposite directions. State the effect of the forces if the two forces act at two different points of the body at a separation $r$. Which of the following is/are true?

  1. Resultant force $=0$

  2. moment of forces $=Fr$

  3. The forces tend to rotate the body about the mid-point between the two forces.

  4. All of the above


Correct Option: D
Explanation:

Here we apply two forces of same magnitude but opposite in direction.Hence we have F and - F which makes resultant force as zero.


Moment of force for F is $r \times F $. For force F it has distance r therefore it has moment rF and same with force -F.Hence moment of force is rF.

The forces tend to rotate the body about the mid-point between the two forces.

Consider a cylindrical shaft of length $\lambda$ and radius $R$. It is twisted by torque r. If shear modulus of material is $S$, then angle of twist should be.

  1. $\theta =\dfrac { \pi SR^{ 4 } }{ 2\tau \ell } $

  2. $\theta =\dfrac { 2\tau }{ \pi S\ell S^{ 4 } } $

  3. $\theta =\dfrac { 2\tau \ell }{ \pi SR^{ 2 } } $

  4. $\theta =\dfrac { 2\tau \ell }{ \pi SR^{ 4 } } $


Correct Option: D

A body is acted upon by two unequal forces in opposite directions, but not in same line. The effect is that:

  1. the body will have only the rotational motion.

  2. the body will have only the translational motion.

  3. the body will have neither the rotational motion nor the translational motion.

  4. the body will have rotational as well as translational motion.


Correct Option: D
Explanation:

Due to unequal forces, the net force will act on the body, so the forces are unbalanced and the unbalanced forces cause a change in motion. This means body having translational motion.
There also be torque acting on the body due to unbalanced force. So there will be rotational motion too.

A uniform meter rule is pivoted at its mid-point. A weight of $50gf$ suspended at one end of it. Where should a weight of $100 gf$ be suspended to keep the rule horizontal : 

  1. At distance $50  \ cm$ from the pivoted end.

  2. At distance $12.5 \ cm$ from the other end.

  3. At distance $37.5 \  cm$ from the other end.

  4. At distance $25 \ cm$ from the pivoted end.


Correct Option: D
Explanation:

As we have one meter rule pivoted at midpoint there will be a perpendicular distance of 50 cm from the contact of force of 50gf.
 Here we have moment of force of $r \times F$.
After substituting we get $moment\ of\ force = 50\times50 gf cm$.
Here this must be balanced by 100gf's moment of force.
 Let us think that there would be x perpendicular distance.
On equating we get 
$ 50\times50  gf cm = 100\times x gf cm$
$ x = 50\times 50/100 = 25 cm$. 

Hence $100 gf$ must be applied at a distance of $25 cm $.

A body is acted upon by two forces each of magnitude $F$, but in opposite directions. State the effect of the forces if both forces act at the same point of the body. Which of the following is/are true?

  1. Resultant force $=0$

  2. Moment of forces $=0$

  3. No motion

  4. All of the above


Correct Option: D
Explanation:

Here, we are applying two force in same magnitude but in opposite that is one is F and -F. Hence resultant force is $F + (-F) = 0 $. 

Hence, resultant force is zero. Here perpendicular distance is same for both the forces.
Hence, if we calculate $r \times F$ cross product. We get the same magnitude of moments but opposite in direction as force are of opposite in direction. Hence moments are also zeroes. Without any resultant and moment there will be no motion.

Name the factor on which moment of inertia of a body depends .

  1. Mass

  2. Force

  3. Distance from rotating axis.

  4. Density


Correct Option: A,C
Explanation:

Moment of inertia of a body depends  on the body's mass distribution and the axis of rotation.
The moment of inertia of a body is directly proportional to its mass and increases as the mass is moved further from the axis of rotation.
Answer (A) 
Mass & (C) Distance from rotating axis.

A uniform metre rule of mass $100g$ is balanced on a fulcrum at mark $40cm$ by suspending an unknown mass $m$ at the mark $20cm$ . To which side the rule will tilt if the mass $m$ is moved to the mark $10cm$?

  1. on the side of mass $m$

  2. on the other side of mass $m$

  3. can't say

  4. it won't tilt


Correct Option: A
Explanation:

As 100 g is balanced at fulcrum it will have a perpendicular distance of 40 cm from itself and mass m will have $100 - 20 = 80 cm $.


Here moment of forces are equal that is balance each other.Hence $ m\times 80 = 100\times  40 \Rightarrow $

$ m = 100/2 = 50 g $.

If there is mark at 10 cm then perpendicular distance would be 90 cm and moment of force would be $50\times90 = 4500\times g \ dyne - cm$ 
where as first moment of force is $100\times40 = 400\times g\ dyne- cm $. 

Hence it tilts on mass m side as it has more moment of force.

Which of the following playground equipment make use of the turning effect of forces?

  1. See-saw

  2. Slide

  3. Swing

  4. Sand-box


Correct Option: A,C
Explanation:

The forces acting on the see-saw and swing produces torque and make them to rotate. See-saw and Swing make use of the effect of forces.

A small piece of space junk is at rest in outer space. A very small asteroid strikes it, exerting a force on it that is NOT directed through the piece of space junk's center of mass.
Which of the following describes the motion of the piece of space junk DURING the asteroid strike?

  1. Because the asteroid is small, the space junk remains at rest

  2. The piece of space junk spins, but does NOT move linearly

  3. The piece of space junk moves at constant velocity linearly, but does NOT spin

  4. The piece of space junk accelerates linearly, but does NOT spin

  5. The piece of space junk accelerates linearly, AND spins


Correct Option: A
Explanation:

Due to striking the space junk, the asteroid will exert a force on the junk piece.

This force is not directed towards the of mass of the junk.
Hence the junk would experience a linear acceleration given by $a=\dfrac{F}{m}$
And also the angular acceleration as provided by the force=$\dfrac{Fl}{I}$
where $l$ is the least distance between the center of mass of junk and line along which asteroid moves,
and $I $ is the moment of inertia of the space junk.

A body is under the action of two equal and oppositely directed forces and the body is rotating with constant non-zero angular acceleration. Which of the following cannot be the separation between the lines of action of the forces?

  1. $1m$

  2. $0.4m$

  3. $0.25m$

  4. zero


Correct Option: D
Explanation:

A pair of equal and opposite forces acting on a body is called a couple.

It only gives a rotating effect to the body and the torque due to a couple is
given by $\tau = Fd$
where $F$ is equal to the  magnitude of one of the forces and 
$d$ is the distance between their points of application.
To produce a non-zero angular acceleration , the torque on the body must be non zero.
Hence , the couple can give a non-zero angular acceleration to the body
only when the distance between the points of applications of the forces is non-zero.   

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