Q. No.A solid cylinder of mass \(3\) kg is rolling on a horizontal surface with a velocity of \(4\) ms-1. It collides with a horizontal spring of force constant \(200\) Nm-1. The maximum compression produced in the spring will be:
1. \(0.5\) m
2. \(0.6\) m
3. \(0.7\) m
4. \(0.2\) m
1. \(0.5\) m
2. \(0.6\) m
3. \(0.7\) m
4. \(0.2\) m
Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are \(v\) and \(2v\) at any instant, then the speed of the centre of mass of the system will be:
1. \(2v\)
2. \(0\)
3. \(1.5v\)
4. \(v\)
If \(\vec F\) is the force acting on a particle having position vector \(\vec r\) and \(\vec \tau\) be the torque of this force about the origin, then:
| 1. | \(\vec r\cdot\vec \tau\neq0\text{ and }\vec F\cdot\vec \tau=0\) |
| 2. | \(\vec r\cdot\vec \tau>0\text{ and }\vec F\cdot\vec \tau<0\) |
| 3. | \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau=0\) |
| 4. | \(\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0\) |
The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:
| 1. | \(\sqrt{3}:\sqrt{2}\) | 2. | \(1:\sqrt{2}\) |
| 3. | \(\sqrt{2}:1\) | 4. | \(\sqrt{2}:\sqrt{3}\) |
The moment of inertia of a uniform circular disc of radius \(R\) and mass \(M\) about an axis touching the disc at its diameter and normal to the disc is:
1.
2.
3.
4.
A solid cylinder of mass \(2~\text{kg}\) and radius \(4~\text{cm}\) is rotating about its axis at the rate of \(3~\text{rpm}.\) The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6~\text{N-m}\)
2. \(2\times 10^{-6}~\text{N-m}\)
3. \(2\times 10^{-3}~\text{N-m}\)
4. \(12\times 10^{-4}~\text{N-m}\)
A disc of radius \(2~\text{m}\) and mass \(100~\text{kg}\) rolls on a horizontal floor. Its centre of mass has a speed of \(20~\text{cm/s}\). How much work is needed to stop it?
1. \(1~\text{J}\)
2. \(3~\text{J}\)
3. \(30~\text{J}\)
4. \(2~\text{J}\)
The angular displacement() of the blades of
a ceiling fan, when the fan is switched on at
t = 0, is shown in figure. The average angular
velocity of the fan blades during the first 8
seconds will be
1. 40 rad/s
2. 20 rad/s
3.10 rad/s
4. 5 rad/s
Three identical spherical shells, each of mass \(m\) and radius \(r\) are placed as shown in the figure. Consider an axis \(XX',\) which is touching two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about the \(XX'\) axis is:
| 1. | \(\dfrac{11}{5}mr^2\) | 2. | \(3mr^2\) |
| 3. | \(\dfrac{16}{5}mr^2\) | 4. | \(4mr^2\) |
A mass \(m\) moves in a circle on a smooth horizontal plane with velocity \(v_0\) at a radius \(R_0.\) The mass is attached to a string that passes through a smooth hole in the plane, as shown in the figure.
The tension in the string is increased gradually and finally, \(m\) moves in a circle of radius \(\frac{R_0}{2}.\) The final value of the kinetic energy is:
| 1. | \( m v_0^2 \) | 2. | \( \dfrac{1}{4} m v_0^2 \) |
| 3. | \( 2 m v_0^2 \) | 4. | \( \dfrac{1}{2} m v_0^2\) |
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