Tag: motion around us

Questions Related to motion around us

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 } $

Show answer
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. $14 \ ms^{-1}$

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

Show answer
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.

A boy of mass $m$ is at one end of a flat boat of mass $M$ and length $l$ which floats stationary on water. If boy moves to the other end,

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

  1. The boat moves in opposite direction through a distance $d = \dfrac { m l } { ( M + m ) }$

  2. The displacement of boy with respect to ground is $d ^ { 1 } = \dfrac { - M } { ( M + m ) }$

  3. The displacement of boy with reject to ground is $d^{2}=\dfrac{-M}{(M+m)}$

  4. The displacement of boy with reject to ground is$d^{3}=\dfrac{-m}{(m+M)}$

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Correct Option: B

A stone is dropped under gravity from rest from a height h and it travels a distance $\frac { 9h }{ 25 } $ in the last second. What is the height 'h' ?

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

  1. 145 m

  2. 100 m

  3. 200m

  4. 300m

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Correct Option: C

Four identical sphere each of radius $10 cm$ and mass $1 kg$ are plaed on a horizontal surface touching one another so that their centres are located at the corners of square of side $20 cm.$ What is the distance of their centre of mass from centre of either sphere$?$

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

  1. $5 cm$

  2. $10 cm$

  3. $20 cm$

  4. none of these

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Correct Option: C

The position of a particle moving along x-axis is given as $x = 3t^2 - t^3$ , in SI units. The distance travelled by the particle in $4$ seconds, is

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

  1. $16\ m$

  2. $24\ m$

  3. $30\ m$

  4. $36\ m$

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Correct Option: A