System of Particles and Rotational Motion · Question 6

A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is: [figure]

1. 757
2. 764
3. 78
4. 740

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm2. The length of the 400 g rod is nearly:

1. 8.5 cm
2. 17.5 cm
3. 20.7 cm
4. 72.0 cm

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively)? [figure]

1. Point P moves slower than point Q
2. Point P moves faster than point Q
3. Both the points P and Q move with equal speed
4. Point P has zero speed

The radius of gyration of a solid sphere of mass 5 kg about XY is 5 m as shown in figure. The radius of the sphere is 5x 7 m, then the value of x is: [figure]

1. 5
2. 2
3. 3
4. 5

The ratio of radius of gyration of a solid sphere of mass M and radius R about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :-

1. 5:3
2. 2:5
3. 5: 3
4. 3: 5

The angular acceleration of a body, moving along the circumference of a circle, is :

1. along the radius towards the centre
2. along the tangent to its position
3. along the axis of rotation
4. along the radius, away from centre

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s2 is

1. 2
2. 4
3. 12
4. 104

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is :

1. 103 m
2. 203 m
3. 10 m
4. 5 m

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

1. 2 : 1
2. 2 : 1
3. 4 : 1
4. 1 : 2

An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :

1. 0.07 kg m2
2. 0.7 kg m2
3. 3.22 kg m2
4. 30.8 kg m2