Physics

Rotational and Circular Motion

235 Questions

Rotational and circular motion examines the dynamics of objects moving in circular paths or rotating around an axis. Key concepts include angular momentum, torque, moment of inertia, and centripetal force. This is a highly scoring topic in the physics section of competitive exams.

Angular momentumCentripetal forceMoment of inertiaRolling objectsGyroscopic effect

Rotational and Circular Motion Questions

Multiple choice physics light : reflection and refraction from plane surface introduction to light and mirror magic with mirrors image formation by plane mirror principle of reversibility of path of light refractive index

A flat mirror revolves at a constant angular velocity making $n=0.4$ revolutions per second. With what velocity (in $ms^{-1}$ ) will a light spot move along a spherical screen with a radius of $15$ metres, if the mirror is at the centre of curvature of the screen?

  1. $37.7$
  2. $60.3$
  3. $68.7$
  4. $75.4$
  5. $90.4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$\because$ Angular velocity of mirror = $0.4rev/s$
$\Rightarrow 0.4\times 2\pi=0.8\pi\,rad/s$
$\because$ Angular velocity of reflected ray
$\Rightarrow 2\times 0.8\pi=1.6\pi\,rad/s$
Hence, velocity of light spot over the screen
$v=rw=15\times 1.6\pi=75.4m/s$
Multiple choice physics along with motion different types of motion basics of motion motion and reference point

Which of the following is a type of motion?

  1. Circular

  2. Rectilinear

  3. Periodic

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
'A body is said to be in motion, if it changes its position with respect to its surrounding.'
Example;-Circular motion;"The motion of an object in a circular path is known as circular motion"
Linear motion-"(also called rectilinear motion) is one dimensional motion along straight line"
Periodic motion-Motion repeated in equal intervals of time
Multiple choice lorentz transformation and muon experiment option a: relativity physics

An experimenter measures the length of a rod. In the cases listed, all motions are with respect to the lab and parallel to the length of the rod. In which of the cases the measured length will be minimum?

  1. The rod and the experimenter move with the same speed v in the same direction.

  2. The rod and the experimenter move with the same speed v in opposite directions.

  3. The rod moves at speed v but the experimenter stays at rest.

  4. The rod stays at rest but the experimenter moves with the speed v.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The rod and the experimenter move with the same speed v in opposite directions, as if a rod is moving with speed parallel to its length, and when the rod and the experimenter move with the same speed $\nu$ in opposite direction the new $\nu$ will be $2\nu$, as the velocity adds up and hence the length will be minimum in this case.
Multiple choice lorentz transformation and muon experiment option a: relativity physics

An experimenter measures the length of a rod. Initially the experimenter and the rod are at rest with respect to the lab. Consider the following statements.
(A) If the rod starts moving parallel to its length but the observer stays at rest, the measured length will be reduced.
(B) If the rod stays at rest but the observer starts moving parallel to the measured length of the rod, the length will be reduced.

  1. A is true but B is false.

  2. B is true but A is false.

  3. Both A and B are true.

  4. Both A and B are false.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to special relativity, length contraction is relative. Whether the rod moves or the observer moves, the measured length of the rod in the frame where it is moving is L = L_0 / gamma. Both statements describe the same physical phenomenon from different frames.

Multiple choice examples of circular motion uniform circular motion circular motion and gravitation physics

A very small particle rests on the top of a hemisphere of radius $20\ cm$. The smallest horizontal velocity to be given to it, if it is to leave the hemisphere without sliding down its surface taking $g = 9.8 m/s^{2}$ is:

  1. $\sqrt{9.8}\ m/s$
  2. $\sqrt{4.9}\ m/s$
  3. $\sqrt{1.96}\ m/s$
  4. $\sqrt{3.92}\ m/s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Critical velocity at the top most point is $\sqrt{g\ell}$
$\therefore$ smallest velocity, such that the particle just leaves the surface =$\sqrt{9.8\times 0.2}=\sqrt{1.96}=1.4\ ms^{-1}$

Multiple choice examples of circular motion uniform circular motion circular motion and gravitation physics

The minimum centripetal force required to rotate a body mass $m$ in a vertical circle of radius $r$ is

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

  4. Zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The tension at the top-most point would be zero in the critical case that the particle just completes the verticle circle without being slake. The minimum centripetal force would then be equal to the force due to gravity $=mg$


Multiple choice examples of circular motion uniform circular motion circular motion and gravitation physics

An inclined plane ends into vertical loop of radius $R$. A particle is released from height $3R$. Can it loop the loop?

  1. yes

  2. no

  3. cannot say

  4. yes if fraction is present
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The minimum speed required at the bottom of the circle(r) to complete the circular motion is $\sqrt {5gR}$
For this speed, the minimum height required is
$0.5mv^2=mgh$
$\Rightarrow 0.5(5gR)=gh$
$\Rightarrow h=\dfrac {5}{2}R$
So, the minimum height from which the body has to released is 2.5R. We have a height of 3R, so the particle completes the vertical loop.
Option A.

Multiple choice examples of circular motion uniform circular motion circular motion and gravitation physics

The maximum tension that an inextensible ring of radius 1 m and mass density 0.1 kg ${ m }^{ -1 }$ can bear is 40 N . The maximum angular velocity with which it can be rotated in a  circular path is 

  1. 20 rad/s

  2. 18 rad/s

  3. 16 rad/s

  4. 15 rad/s
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a rotating ring, the tension T = lambda * v^2 = lambda * (omega * R)^2. Given T = 40 N, lambda = 0.1 kg/m, R = 1 m: 40 = 0.1 * omega^2 * (1)^2. omega^2 = 400, so omega = 20 rad/s.

Multiple choice examples of circular motion uniform circular motion circular motion and gravitation physics

A body is allowed to slide on a frictionless track from rest under-gravity.The track ends in a circular of diameter D. What should be the mini-mum height of the body in terms of D.          So that it may successfully complete the loop?

  1. $\dfrac{9}{4}D $
  2. $ \frac {5}{4} D $

  3. D

  4. 2 D
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Velocity at top of the circle is $\sqrt{5gr}$ 

Energy lost to reach height D from height H  $ = mg(H-D)$

Energy gained in the form of $K.E= \dfrac12 mv^2= \dfrac12 m(5gr) = \dfrac{5mgD}{4}$ 

Equating K.E. and P.E. ,

$\dfrac{5mgD}{4} = mg(H-D)$

$H=\dfrac{9D}{4}$

Multiple choice examples of circular motion uniform circular motion circular motion and gravitation physics

A body is a allowed to slide down a frictionless track from rest position at its top under gravity. The track ends in a circular loop of diameter $D$. Then, the minimum height of the inclined track  (in terms of $D$ ) so that it may complete successfully the loop is:

  1. $\dfrac{7D}{4}$
  2. $\dfrac{9D}{4}$
  3. $\dfrac{5D}{4}$
  4. $\dfrac{3D}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$V _{0}$ required for a complete vertical circle: $V _{0} =\sqrt{\dfrac{5}{2}gD}$
WET between top and bottom:
              $mgH  = \dfrac{1}{2}m V _{0}^{2}$


                 $gH  = \dfrac{5}{4}gD$

                   $H  = \dfrac{5}{4}D$

Multiple choice examples of circular motion uniform circular motion circular motion and gravitation physics

A weightless thread can bear tension up to $3.7kg-wt$. A stone of mass $500g$ is tied to it and revolved in a circular path of radius $4$m in a verticle plane. If $g=10m/s^2$, then the maximum angular velocity of the stone will be:

  1. $2 rad/s$
  2. $4 rad/s$
  3. $16 rad/s$
  4. $\sqrt{21} rad/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Tension is maximum at lowest point of a verticle circle $T _{max}=mr\omega^2+mg$
$3.7g=0.5\times 4\times \omega^2+0.5g$
$2\omega^2=3.2g$
$\omega=\sqrt{1.6g}=\sqrt{1.6\times 10}$
$\omega=4rad/s$