The moment of inertia of a thin uniform circular disc about one of its diameter is I. Its moment of inertia about an axis perpendicular to the circular surface and passing through its center will be:

1. $\sqrt{2}I$

2. 2 l

3. $\frac{I}{2}$

4. $\frac{I}{\sqrt{2}}$

A child is standing on the edge of a merry-go-round that has the shape of a disk, as shown in the figure. The mass of the child is 40 kilograms. The merry-go-round has a mass of 200 kilograms and a radius of 2.5 meters, and it is rotating with an angular velocity of $\omega =2.0$ radians per second. The child then walks slowly towards the center of the merry-go-round. When the child reaches the center, what is the angular velocity of the disc? (The size of the child can be neglected.)
     
1. 2.0 rad/s

2. 2.2 rad/s

3. 2.4 rad/s

4. 2.8 rad/s

A man 'A', mass 60 kg, and another man 'B', mass 70 kg, are sitting at the two extremes of a 2 m long boat, of mass 70 kg, standing still in the water as shown. They come to the middle of the boat. (Neglect friction). How far does the boat move on the water during the process?

A uniform rod of length 1 m and mass 2 kg is suspended by two vertical inextensible strings as shown in following figure. Calculate the tension T (in newtons) in the left string at the instant when the right string snaps (g = 10 m/$s^2$).
       
1. 2.5 N

2. 5 N

3. 7.5 N

4. 10 N

A uniform beam, \(3.0\) m long, of weight \(100\) N has a \(300\) N weight placed \(0.5\) m from one end. The beam is suspended by a string \(1.0\) m from the same end. A diagram of the weights placed on the beam is given below:
           
How far from the other end must a weight of \(80\) N be placed for the beam to be balanced?

A horizontal heavy uniform bar of weight \(W\) is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to:

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D${}_1$ has a 2 kg mass, 0.2 m radius, and an initial angular velocity of 50 rad s${}^{-1}$. Disc D${}_2$ has 4 kg mass, 0.1 m radius, and initial angular velocity of 200 rad s${}^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s${}^{-1}$) of the system will be:

1. 60

2. 100

3. 120

4. 40

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along:

A circular platform is mounted on a frictionless vertical axle. Its radius is R = 2m and its moment of inertia about the axle is 200 kg m². Initially, it is at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at a speed of 1 m s^–1 relative to the ground. The time taken by the man to complete one revolution is:
1. $\mathrm{\pi } \sec$                 
2. $\frac{3\mathrm{\pi }}{2}\sec$
3. $2\mathrm{\pi } \sec$               
4. $\frac{\mathrm{\pi }}{2}\sec$