Physics - Rotational Motion and Moment of Inertia
Exam Duration: 45 Mins Total Questions : 30
In a system of N-particles at equilibrium, the net linear momentum of the system about centre of mass is
- (a)
zero
- (b)
constant
- (c)
maximum
- (d)
minimum
A gramophone turn table have the angular speed 150 rpm slows down uniformly and stops in 10 s after breaking the supply to the motor. The angular acceleration in rad per square second is
- (a)
2.57
- (b)
6.81
- (c)
-1.57
- (d)
-2.57
A sphere of mass m and radius r rolls with slipping on the surface. At any time its translational and rotational velocities are v0 and \(\frac { { v }_{ 0 } }{ 2r } \), respectively. The speed (translation) at the instant when the mass just starts the pure rolling, is
- (a)
\(\frac { 6 }{ 5 } { v }_{ 0 }\)
- (b)
\(\frac { 6 }{ 7 } { v }_{ 0 }\)
- (c)
\(\frac { 3 }{ 7 } { v }_{ 0 }\)
- (d)
\(\frac { 9 }{ 7 } { v }_{ 0 }\)
The moment of inertia of uniform semi - circular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is
- (a)
\(\frac { 1 }{ 4 } { Mr }^{ 2 }\)
- (b)
\(\frac { 2 }{ 5 } { Mr }^{ 2 }\)
- (c)
\({ Mr }^{ 2 }\)
- (d)
\(\frac { 1 }{ 2 } { Mr }^{ 2 }\)
Two particles of masses m1 and m2 separated by a distance d are at rest initially. If they move towards each other under mutual interaction (say electric, gravitational or elastic), where will they meet?
- (a)
At the centre of line joining the two particles
- (b)
Anywhere in between two masses
- (c)
At the centre of mass of the system of two particles
- (d)
None of the above
Particles of masses m, 2m, 3m, ... , nm grams are placed on the same line at distances l,2l,3l, ... ,nl cm from a fixed point. The distance of the centre of mass of the particles from the fixed point (in centimetres) is:
- (a)
\({(2n+1)l\over3}\)
- (b)
\({l\over n+1}\)
- (c)
\({n(n^2+1)l\over 2}\)
- (d)
\({2l\over n(n^2+1)}\)
A uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to
the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length; then:
- (a)
L = R
- (b)
\(L=\sqrt { 3 } R\)
- (c)
\(L=\frac { R }{ \sqrt { 3 } } \)
- (d)
L = 0
The moment of inertia of a sphere is 20 kg-m2 about the diameter. What is the moment of inertia about any tangent?
- (a)
25 kg-m2
- (b)
50 kg-m2
- (c)
70 kg-m2
- (d)
80 kg-m2
If a particle moves in the X Y-plane, the resultant angular momentum has:
- (a)
only x-component
- (b)
only y-component
- (c)
both x and y-components
- (d)
only z-component
A homogeneous disc with a radius 0.2 m and mass 5 kg rotates around an axis passing through its centre. The angular velocity of the rotation of the disc as a function of time is given by the formula \(\omega\) = 2 + 6t. The tangential force applied to the rim of the disc is:
- (a)
1N
- (b)
2N
- (c)
3N
- (d)
4N
The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height h, from rest, without sliding is:
- (a)
\(\sqrt{gh}\)
- (b)
\(\sqrt{(6/5)gh}\)
- (c)
\(\sqrt{(4/3)gh}\)
- (d)
\(\sqrt{(10/7)gh}\)
The moment of inertia of a solid cylinder about its axis is I. It is allowed to roll down an inclined plane without slipping. If its angular velocity at the bottom be to, then kinetic energy of the cylinder will be:
- (a)
\({1\over2}I\omega^2\)
- (b)
\(I\omega^2\)
- (c)
\({3\over2}I\omega^2\)
- (d)
2\(I\omega^2\)
A rod of mass M and length L is suspended freely from its end and it can oscillate in the vertical plane about the point of suspension. It is pulled to one side and then released. It
passes through the equilibrium position with angular speed \(\omega .\) What is its kinetic energy while passing through the mean position?
- (a)
\(ML^2\omega^2\)
- (b)
\(ML^2\omega^2/4\)
- (c)
\(ML^2\omega^2/6\)
- (d)
\(ML^2\omega^2/12\)
A wheel having a rotational inertia of 0.20 kg-m2 rotates at 360 rpm a bout a vertical axis. What is the angular speed of the wheel when a torque of -I N-m is applied about the same axis for 3.0 sec?
- (a)
12.68 rad/sec
- (b)
22.68 rad/sec
- (c)
32.68 rad/sec
- (d)
42.68 rad/sec
Two equal and opposite forces act on a rigid body at a certain distance. Then
- (a)
the body is in equilibrium
- (b)
the body will rotate about its centre of mass
- (c)
the body may rotate about any point other than its centre of mass
- (d)
the body cannot rotate about its centre of mass
A thin hollow sphere of mass m is completely filled with a liquid of mass m. When the sphere rolls with a velocity u, kinetic energy of the system is equal to:
- (a)
\({1\over2}mv^2\)
- (b)
\(mv^2\)
- (c)
\({4\over3}mv^2\)
- (d)
\({4\over5}mv^2\)
A body of mass 20 kg is moving with a velocity of 2v and another body of mass 10 kg is moving with velocity v. The velocity of their centre of mass is :
- (a)
5v/3
- (b)
2v/3
- (c)
v
- (d)
zero