Physics - Rotational Motion and Moment of Inertia
Exam Duration: 45 Mins Total Questions : 30
For a rotating body if 'a' is tangential acceleration; \(\vartheta \) linear speed, \(\alpha\) angular acceleration and \(\omega\) angular velocity, then \(\alpha /a\) is
- (a)
\(\omega /\vartheta \)
- (b)
\(\vartheta /\omega \)
- (c)
\(\vartheta \omega \)
- (d)
\({ (\vartheta \omega ) }^{ -1 }\)
A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. Its angular speed will
- (a)
increase approximately by 1%
- (b)
decrease approximately by 1%
- (c)
decrease approximately by 0.67%
- (d)
decrease approximately by 0.33%
The angular displacement at any time t is given by \(\theta\)(t) = 2t3 - 6t2 . The torque on the wheel will be zero at
- (a)
1 s
- (b)
0.1 s
- (c)
2 s
- (d)
0.2 s
Match the parameter given in column I with their definition/formula given in column II select the correct option from the choices given.
Column I | Column II | ||
A. | Centre of mass | 1. | Rotation + Translation |
B. | Parallel axis theorem | 2. | A hypothetical point where the entire mass of the body is supposed to be concentrated |
C. | Rolling motion | 3. | IP = ICM + Mr2 |
- (a)
A B C 1 2 3 - (b)
A B C 3 1 2 - (c)
A B C 2 3 1 - (d)
A B C 2 1 3
A system consists of two identical particles. One particle is at rest and the other particle has an acceleration a. The centre of mass of the system has an acceleration of:
- (a)
2a
- (b)
a
- (c)
\({a\over2}\)
- (d)
\({a\over4}\)
Mass is non-uniformly distributed on the circumference of a ring of radius a and centre at origin. Let b be the distance of the centre of mass of the ring from origin. Then:
- (a)
b = a
- (b)
\(0\le b\le a\)
- (c)
b < a
- (d)
B > a
Angular momentum of a body is defined as the product of:
- (a)
mass and angular velocit
- (b)
centripetal force and radius
- (c)
linear velocity and angular velocity
- (d)
moment of inertia and angular velocity
A mass is revolving in a circle which is in the plane of paper. The direction of angular acceleration is:
- (a)
upward the radius
- (b)
towards the radius
- (c)
tangential
- (d)
at right angle to angular velocity
A body of mass M and radius R is rolling horizontally without slipping with speed v. It then rolls up a hill to a maximum height h. If h = 5 v2 /6 g, what is the M.l. of the body?
- (a)
\({1\over2}MR^2\)
- (b)
\({2\over3}MR^2\)
- (c)
\({3\over4}MR^2\)
- (d)
\({2\over5}MR^2\)
A uniform sphere of mass 200 gm rolls without slipping on a plane surface so that its centre moves at a speed of 2.00 cm/sec. Its KE is:
- (a)
5.6 x 10-5 J
- (b)
5.6 x 10-4 J
- (c)
5.6 x 10-3 J
- (d)
5.6 x 10-2 J
A thin hollow cylinder is free to rotate about its geometrical axis. It has a mass of 8 kg and a radius of 20 cm. A rope is wrapped around the cylinder. What force must be exerted along the rope to produce an angular acceleration of 3 rad/sec2?
- (a)
8.4N
- (b)
5.8N
- (c)
4.8N
- (d)
None of these
Two identical solid cylinders run a race starting from rest at the top of an inclined plane. If one cylinder slides and the other rolls:
- (a)
the sliding cylinder will reach the bottom first with greater speed
- (b)
the rolling cylinder will reach the bottom first with greater speed
- (c)
both will reach the bottom simultaneously with the same speed
- (d)
both will reach the bottom simultaneously but with different speeds
A cord is bound round the circumference of a wheel of radius R. The axis ofthe wheel is horizontal and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling through distance h, the angular velocity of the wheel will be:
- (a)
\([{2gh\over I+mr}]^{1/2}\)
- (b)
\([{2mgh\over I+mr^2}]^{1/2}\)
- (c)
\([{2mgh\over I+2m}]^{1/2}\)
- (d)
\(\sqrt{2gh}\)
A disc of moment of inertia I1 is rotating freely with angular velocity \(\omega_1\) when a second, non-rotating disc with moment of inertia I2 is dropped on it gently the two then rotate as a unit. Then the total angular speed is:
- (a)
\({I_1\omega_1\over I_2}\)
- (b)
\({I_2\omega_1\over I_1}\)
- (c)
\({I_1\omega_1\over I_2+I_1}\)
- (d)
\({(I_1+I_2)\omega_1\over I_2}\)
If the earth suddenly stops revolving and all its rotational KE is used up in raising its temperature and if s is taken to be the specific heat of the earth's material, the rise of temperature ofthe earth will be: (R = radius ofthe earth and \(\omega\) = its angular velocity)
- (a)
\({R^2\omega^2\over 5Js}\)
- (b)
\({R^2\omega^2\over 5J}\)
- (c)
\({R^2\omega\over 5Js}\)
- (d)
\({R^2\omega^2\over 5s}\)
Two bodies of mass l kg and 3 kg have position vectors \(\hat{i}+2\hat{j}+\hat{k}\) and \(-3\hat{i}-2\hat{j}+\hat{k}\)respectively. The centre of mass ofthis system has a position vector:
- (a)
\(-2\hat{i}-\hat{j}+\hat{k}\)
- (b)
\(2\hat{i}-\hat{j}-2\hat{k}\)
- (c)
\(-\hat{i}+\hat{j}+\hat{k}\)
- (d)
\(-2\hat{i}+2\hat{k}\)
A body of mass m and radius r is released from rest along a smooth inclined plane of angle of inclination \(\theta\), The angular momentum of the body about the instantaneous point of contact after a time t from the instant of release is equal to:
- (a)
mgrt cos \(\theta\)
- (b)
mgrt sin \(\theta\)
- (c)
(3/2) mgrt sin \(\theta\)
- (d)
none of these
The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is
- (a)
MR2
- (b)
\({1\over2}\)MR2
- (c)
\({3\over2}\)MR2
- (d)
\({7\over2}\)MR2
A body rolls down an inclined plane. Ifits kinetic energy of rotation is 40% of its kinetic energy of translation, then the body is
- (a)
solid cylinder
- (b)
solid sphere
- (c)
disc
- (d)
ring
A solid sphere is rotating about a diameter at an angular velocity \(\omega\). If it cools so that its radius reduces to \(1\over n\)of its original value, its angular velocity becomes:
- (a)
\({\omega \over n}\)
- (b)
\({\omega \over n^2}\)
- (c)
\({ n \omega}\)
- (d)
\({ n^2 \omega}\)
A system consisting of two masses connected by a massless rod lies along the x-axis. A 0.4 kg mass is at a distance x = 2 m, while a 0.6 kg mass is at a distance x = 7 m. The x-co-ordinate of the centre of mass is:
- (a)
5m
- (b)
3.5m
- (c)
4.5m
- (d)
4m
- (e)
3m