Tag: motion and measurement of distances

Questions Related to motion and measurement of distances

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

A boy running at an average speed of $4 km hr^{-1}$ reaches school from his home in $\frac{1}{2}hr$. The distance of the school from his home is

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

  1. $2 km$

  2. $8 km$

  3. $4 km$

  4. $6 km$

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Correct Option: A
Explanation:

Given:$v =4\frac{Km}{h}$
           

     $t =\dfrac{1}{2}$hour
   as $v=\dfrac{Distance}{t}$
        $Distance=4\times\dfrac{1}{2}$
        $Distance=2Km$

If the displacement of an object is zero, the actual distance traversed by it will be :

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

  1. Zero

  2. Infinite

  3. May not be zero

  4. None of these

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Correct Option: C
Explanation:

Displacement is the distance between the initial and final position of an object. When an object moves in a circular path of radius R, its displacement will be zero but the distance traveled by the object will be the perimeter i.e $2\pi R$. 

Thus, if displacement of an object is zero, the distance traversed by it may not be zero.

Sunil and Rohit start at one end of a street, the origin and run to the other end, then head back. On the way back, Sunil is ahead of Rohit. Which statement is correct about the distances run and the displacements from the origin before reaching the origin?

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

  1. Sunil has run a greater distance and his displacement is greater than Rohit's

  2. Rohit has run a greater distance and his displacement is greater than Sunil's

  3. Sunil has run a greater distance but his displacement is lesser that Rohit's

  4. Rohit has run a greater distance but his displacement is lesser than Sunil's

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Correct Option: C
Explanation:

Before reaching origin, distance travelled by Sunil is more than Rahul since he is ahead of Rohit. But displacement of Rohit is more as he is far from the origin than Sunil.

A free falling body travels ___ of total distance in 5th second.

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

  1. 8 %

  2. 12 %

  3. 25 %

  4. 36 %

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Correct Option: D
Explanation:
The correct option is D

Given,

A free falling body 

Distance traveled in 5s

$S=ut+\dfrac{1}{2}gt^2$ since $u=0,g=10m/s$

$=\dfrac{1}{2}\times10\times5^2$

$=12m$

Distance travelled in 5^th sis:

Distance travelled in 5s- Distance travelled in 4s

Distance travelled in $4s=\dfrac{1}{2}\times10\times4^2$

$=80m$

So,

$s _5-s _4=125-80=45$

Therefore,

$\dfrac{s _5-s _4}{s _5}\times100=\dfrac{45}{125}\times100=36\%$

A particle experiences a constant acceleration for $6s$ after starting from rest. If it travels  distance $x _{1}$ in the first two seconds and a distance $x _{2}$ in the next two next seconds and $x _{3}$in the next two seconds the n  $x _{1}: x _{2}; x _{3}::1:3:5.$

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