Tag: motion and measurement of distances

Questions Related to motion and measurement of distances

A platform is moving in upward direction with uniform velocity 40 ${ ms }^{ -1 }$. When it reaches at a height of 100 m from the ground, a pocket is dropped  from it. The total distance traveled by pocket during its free fall is (Take $g=10{ ms }^{ -2 }$) 

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. 160 m

  2. 260 m

  3. 180 m

  4. 300 m

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Correct Option: C

What does the odometer of an automobile measure?

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. Speed

  2. Distance

  3. Acceleration

  4. All

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Correct Option: B
Explanation:

An odometer or odograph is an instrument that indicates distance traveled by the automobile

A laser signal sent towards the moon returns after t seconds.If c is speed of light, then the distance of the moon from the observer is

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. ct

  2. $ct^{-1}$

  3. $ct^{-2}$

  4. $\displaystyle \frac{ct}{2}$

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Correct Option: D
Explanation:

A laser signal sent towards the moon returns after t seconds.

Time taken to reach moon is $\dfrac{time}{2}=\dfrac{t}{2}$
Therefore $distance=speed*time=c*\dfrac{t}{2}$

Distance is a vector quantity. State whether true or false.

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. True

  2. False

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Correct Option: B
Explanation:

Distance is a scalar quantity. So the given statement is false.

Can a moving object cover zero distance?

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. Always

  2. Sometimes

  3. Never

  4. Can't be said from given condition

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Correct Option: C
Explanation:

A moving object always changes its position. Then, it has move along a path with some length.
So, if the body is moving, it will always cover some path which can never have zero length. Thus distance travelled by a moving object can never be zero.

Given 2x = 4, Where x is distance. Find the Value of X.

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. 1

  2. 2

  3. 3

  4. 4

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Correct Option: B
Explanation:

The given equation is  $2x  =4$

Thus  $x  = \dfrac{4}{2} = 2$

State whether given statement is True or False.
Path length is scalar Quantity ?

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. True

  2. False

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Correct Option: A
Explanation:

Path length is distance covered by body in reaching from initial point to final point. It may be different for different paths.

Since path length is distance hence it is scalar quantity, it may be different for two paths with same initial and final points.

The distance of closest approach of an $\alpha $-particle projected towards a nucleus with momentum p is r. What will be the distance of closest approach, when the momentum of projected $\alpha $-particle is 2p?

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. 2r

  2. 4r

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

  4. $\dfrac { r }{ 4 } $

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Correct Option: D
Explanation:

At the distance of closest approach:$KE=PE$

$\dfrac{p^2}{2m}=\dfrac{k 2 eq}{r}$
When the momentum chnages to 2p:
$\dfrac{(2p)^2}{2m}=k\dfrac{2eq}{r'}$
$\dfrac{4p^2}{2m}=k\dfrac{2eq}{r'}$
$\dfrac{2p^2}{m}=k\dfrac{2eq}{r'}$
$r'=k\dfrac{2eq}{p^2} \times \dfrac{m}{2}$
$=\dfrac{r}{2m}\times \dfrac{m}{2}$
$r'=\dfrac{r}{4}$

The height $y$ and horizontal distance $x$ covered by a projectile in a time $t$ seconds are given by the equations $y = 8t - 5t^2$ and $x = 6t$. If $x$ and $y$ are measured in meters, the velocity of projection is:-

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. $10 \ ms^{-1}$

  2. $6 \ ms^{-1}$

  3. $8 \ ms^{-1}$

  4. $14 \ ms^{-1}$

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Correct Option: A
Explanation:

$v _x=\dfrac{dx}{dt}=6$

$v _y=\dfrac{dy}{dt}=8-10t$
$\vec v=v _x\hat{i}+v _y\hat{j}$

$\vec u=\vec v _{t=0}$
$\vec u=6\hat{i}+8\hat{j}$
$u=\sqrt{6^2+8^2}$
$u=10m/s$

Estimate the force exerted by a $75 \ W$ bulb on your finger tip (are $1\ cm^{2}$), when is at a distance of $8 \ cm$ from the bulb. (Assume $100\%$ absorption)

physics motion and measurement of distances motion around us motion and rest moving things around us

  1. $1 \ N$

  2. $3.1 \times 10^{-10} N$

  3. $4 \times 10^{-6} N$

  4. $2 \times 10^{-4} N$

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Correct Option: B
Explanation:

$\begin{array}{l} P=\frac { { \overline { S }  } }{ c } =\frac { { \frac { P }{ { 4\pi { d^{ 2 } } } }  } }{ c } =\frac { { \frac { { 75W } }{ { 4\pi { { \left( { 8.0\times { { 10 }^{ -2 } }m } \right)  }^{ 2 } } } }  } }{ { 3.00\times { { 10 }^{ 8 } }\, m/s } } =3.1\times { 10^{ -6 } }N/{ m^{ 2 } }. \ The\, \, force\, \, is\, \, pressure\, \, times\, \, area, \ we\, \, approximate\, \, the\, \, area\, \, of\, \, a\, \, fingertip\, \, to\, \, be\, \, 1.0\, c{ m^{ 2 } } \ F=PA=\left( { 3.1\times { { 10 }^{ -6 } }N/{ m^{ 2 } } } \right) \left( { 1.0\times { { 10 }^{ -4 } }{ m^{ 2 } } } \right) =3.1\times { 10^{ -10 } }N \end{array}$

Hence,
option $(B)$ is correct answer.