System of Particles and Rotational Motion · Question 1

A thin wire of length 'L' and linear mass density 'm' is bent into a circular ring (in x-y plane) with centre 'C' as shown in figure. The moment of inertia of the ring about an axis yy' will be: [figure]

1. 3mL38
2. 3mL28 2
3. 3mL38 2
4. 3mL28

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre O. Its angular momentum is LA and LB computed about points A and B, respectively, with OB = 2 OA. The value of LALB is: [figure]

1. 2
2. 14
3. 12
4. 1

A solid sphere A of radius R and mass M is attached at a point to a smaller solid sphere B of radius r < R and mass m < M. Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of A is IA and that calculated about a vertical axis passing through the centre of B is IB. The difference IA - IB is: [figure]

1. 0
2. (M - m)(R + r)2
3. (m - M)(R + r)2
4. (m - M)(R - r)2

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of 60 with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (Take g = 10 m/s2)

1. 200 N
2. 200 3 N
3. 100 N
4. 100 3 N

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

1. 115 days
2. 108 days
3. 100 days
4. 105 days

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