JEE Main Physics - Rotational Motion and Moment of Inertia
Exam Duration: 60 Mins Total Questions : 30
Two spheres of masses m1 and m2 (m1 > m2) respectively are tied to the ends of a string which passes over a light frictionless pulley. The masses are initially at rest and released. The acceleration centre of mass is
- (a)
g
- (b)
\(\left( \frac { { m }_{ 1 }-{ m }_{ 2 } }{ { m }_{ 1 }+{ m }_{ 2 } } \right) g\)
- (c)
\({ \left( \frac { { m }_{ 1 }-{ m }_{ 2 } }{ { m }_{ 1 }+{ m }_{ 2 } } \right) }^{ 2 }g\)
- (d)
\(\frac { 1 }{ 2 } { \left( \frac { { m }_{ 1 }-{ m }_{ 2 } }{ { m }_{ 1 }+{ m }_{ 2 } } \right) }^{ 2 }g\)
The centre of mass of a body:
- (a)
depends on the choice of co-ordinate system
- (b)
is independent of the choice of co-ordinate system
- (c)
mayor may not depend on the choice of co-ordinate system
- (d)
none of the above
A system consists of mass M and m (<< M). The centre of mass of the system is:
- (a)
at the middle
- (b)
nearer to M
- (c)
nearer to m
- (d)
at the position of larger mass
Two circular discs A and B are of equal masses and thicknesses but made of metal with densities dA and dB (d A > dB} If their moments of inertia about an axis passing through their centres and perpendicular to circular faces be IA and IB , then:
- (a)
IA = IB
- (b)
IA > IB
- (c)
IA < IB
- (d)
IA \(\ge\) IB
When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is:
- (a)
1 : 7
- (b)
1 : 2
- (c)
1 : 1
- (d)
5 : 7
A wheel, initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle \(\theta\)1 in the first one second and through an additional angle \(\theta\)2 in the next one second. The ratio \(\theta\)2 /\(\theta\)1 is:
- (a)
4
- (b)
3
- (c)
2
- (d)
1
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)
\(\sqrt{(10/7)gh}\)
A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in rad/sec2) of the stick if the string is cut?
- (a)
\({3\over2}g\)
- (b)
g
- (c)
3g
- (d)
4g
A heavy ball is thrown on a rough horizontal surface in such a way that it slides with a speed Vo initially without rolling. It will roll without sliding when its speed falls to:
- (a)
(2/7) Vo
- (b)
(3/7)Vo
- (c)
(5/7) Vo
- (d)
(7/5) Vo
A cylinder is rolling over a surface. Which points on it move rectilinearly?
- (a)
All points on the curved surface of the cylinder
- (b)
All points on the flat surfaces of the cylinder
- (c)
All points on the axis of the cylinder
- (d)
None of the above
A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque \(\tau\) on the ring, it stops after making n revolutions. After how many revolutions will the disc stop if the retarding torque on it is also \(\tau\) ?
- (a)
n/2
- (b)
n
- (c)
2n
- (d)
4n
A sphere of mass M rolls without slipping on an inclined plane of inclination \(\theta\). What should be the minimum coefficient of friction, so that the sphere rolls down without slipping?
- (a)
\({2\over5}tan \theta\)
- (b)
\({2\over7}tan \theta\)
- (c)
\({5\over7}tan \theta\)
- (d)
\(tan \theta\)
The angular momentum of a moving body remains constant if:
- (a)
net external force is applied
- (b)
net pressure is applied
- (c)
net external torque is applied
- (d)
net external torque is not applied
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 circular platform is mounted on a vertical frictionless axle. Its radius is r = 2 m and its moment of inertia is I = 200 kg-m2. It is initially at rest. A 70 kg man stands on the edge of the platform and begins to walk along the edge at speed vo = 1.0 m/s relative to the ground. The angular velocity of the platform is:
- (a)
1.2 rad/s
- (b)
0.4 rad/s
- (c)
2.0 rad/s
- (d)
0.7 rad/s
A tap can be operated easily using two fmgers because:
- (a)
the force by one finger overcomes friction and other finger provides the force for operation
- (b)
the rotational effect is caused by the couple formed
- (c)
the force available for the operation will be more
- (d)
this helps application of angular forces
A particle of mass 0.2 kg is moving in a circle of radius 1m with f = (2/\(\pi\))sec-1, then its angular momentum is:
- (a)
0.8 kg-m2/s
- (b)
2kg-m2/s
- (c)
8kg-m2/s
- (d)
16kg-m2/s
A planet moves around the sun in an elliptical orbit with the sun at one of its foci. The physical quantity associated with the motion of the planet that remains constant with time is :
- (a)
velocity
- (b)
centripetal force
- (c)
linear momentum
- (d)
angular momentum
Two blocks of masses 6 kg and 4 kg are placed on a frictionless surface and connected by a spring. If the heavier mass is given a velocity of 14 m/s in the direction of lighter one, then the velocity gained by the centre of mass will be:
- (a)
7.4 m/s
- (b)
14 m/s
- (c)
8.4 m/s
- (d)
10 m/s