Q. No.
Three masses are placed on the x-axis: \(300\) g at the origin, \(500\) g at \(x =40\) cm, and \(400\) g at \(x=70\) cm. The distance of the center of mass from the origin is:
1.
\(40\) cm
2.
\(45\) cm
3.
\(50\) cm
4.
\(30\) cm
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
1. B
2. C
3. D
4. A
A force F= is acting at a point r=--12. The value of α
for which angular momentum is conserved about the origin is:
1. -1
2. 2
3. zero
4. 1
Two rotating bodies A and B of masses m and 2m with moments of inertia and have equal kinetic energy of rotation. If and be their angular momenta respectively, then:
1.
2.
3.
4.
A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first 2 sec, it rotates through an angle θ1. In the next 2 seconds, it rotates through an additional angle θ2. The ratio of θ2/θ1 is:
| 1. | 1 | 2. | 2 |
| 3. | 3 | 4. | 5 |
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. \(\sqrt{(m_1m_2)}l^2\)
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. | \(w(d-x) \over d\) |
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 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. | \(\frac{\omega M}{M+m}\) |
Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?
| 1. | Moment of inertia | 2. | Angular momentum |
| 3. | Angular velocity | 4. | Rotational kinetic energy |
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