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.
| 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 solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere will be:
1. 7:10
2. 5:7
3. 10:7
4. 2:5
A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?
1. Sphere
2. Both reach at the same time
3. Depends on their masses
4. Disc
| 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
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