A uniform rod of mass 2M is bent into four adjacent semicircles, each of radius r, all lying in the same plane. The moment of inertia of the bent rod about an axis through one end A and perpendicular to the plane of the rod is:
1. 22
2. 88
3. 44
4. 66
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:
1. | \(W\) | 2. | \(W \over 2\) |
3. | \(3W \over 4\) | 4. | \(W \over 4\) |
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.
2. 2 l
3.
4.
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 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
1. | zero | 2. | \(1\) m |
3. | \(2\) m | 4. | \(5\) m |
Five uniform circular plates, each of diameter \(D\) and mass \(m\), are laid out as shown in the figure. Using the origin shown, the \(y\text-\text{coordinate}\) of the centre of mass of the ''five–plate'' system will be:
1. | \(\frac{2D}{5}\) | 2. | \(\frac{4D}{5}\) |
3. | \(\frac{D}{3}\) | 4. | \(\frac{D}{5}\) |
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?
1. | \(5\) cm leftward | 2. | \(5\) cm rightward |
3. | \(7\) cm leftward | 4. | \(7\) cm rightward |
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/).
1. 2.5 N
2. 5 N
3. 7.5 N
4. 10 N
A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity:
1. | \(\frac{\omega(M-2 m)}{M+2 m} \) | 2. | \(\frac{\omega M}{M+2 m} \) |
3. | \(\frac{\omega(M+2 m)}{M} \) | 4. | \(\frac{\omega M}{M+m}\) |