Q. No.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 co–ordinate of the centre of mass of the five–plate system will be:
1.
2D/5
2.
4D/5
3.
D/3
4.
D/5
A boat of length 10 m and a mass of 450 kg is floating without motion in still water. A man of 50 kg standing at one end walks to the other end and comes to a stop. The magnitude of the displacement of the boat relative to the ground is:
| 1. | Zero | 2. | 1 m |
| 3. | 2 m | 4. | 5 m |
1. \(\left(-\frac{15}{7}, \frac{85}{17}, \frac{1}{7}\right) \mathrm{cm}\)
2. \(\left(\frac{15}{7},-\frac{85}{17}, \frac{1}{7}\right) \mathrm{cm}\)
3. \(\left(\frac{15}{7}, \frac{85}{21},-\frac{1}{7}\right) \mathrm{cm}\)
4. \(\left(\frac{15}{7}, \frac{85}{21}, \frac{7}{3}\right) \mathrm{cm}\)
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. | \(W \over 4\) |
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. | \(\frac{\omega M}{M+m}\) |
A solid cylinder of mass \(50\) kg and radius \(0.5\) m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other end hanging freely.
The tension in the string required to produce an angular acceleration of \(2\) revolutions/s2 will be:
1. \(25\) N
2. \(50\) N
3. \(78.5\) N
4. \(157\) N
A rod of weight \(w\) is supported by two parallel knife edges, A and B, and is in equilibrium in a horizontal position. The knives are at a distance \(d\) from each other. The centre of mass of the rod is at a distance \(x \) from A. The normal reaction on A is:
| 1. | \(wx \over d\) | 2. | \(wd \over x\) |
| 3. | \(w(d-x) \over x\) | 4. | \(w(d-x) \over d\) |
1. \(\frac{m_1m_2}{m_1+m_2}l^2\)
2. \(\frac{m_1+m_2}{m_1m_2}l^2\)
3. \((m_1+m_2)l^2\)
4. \(\sqrt{(m_1m_2)}l^2\)
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
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