Physics #restart (Systems of Particles and Rotational Motion SET C -Medium)Contact Number: 8527521718Physics #restart (Systems of Particles and Rotational Motion SET C -Medium)Contact Number: 8527521718Two loads \(P_1\) \(P_2\)\((P_1>P_2)\) are connected by a string passing over a fixed pulley. The center of gravity of loads are initially at the same height. Find the acceleration of the center of gravity of the system:
| 1. | \(\left(\frac{(P_1-P_2)^{\frac{1}{2}}}{P_1+P_2}\right)g\) | 2. | \(\left(\frac{P_1-P_2}{P_1+P_2}\right)g\) |
| 3. | \(\left( \frac{P_1-P_2}{P_1+P_2}\right)^2g\) | 4. | \(\left( \frac{P_1+P_2}{P_1-P_2}\right)g\) |
| 1. | \(\dfrac{\omega_1}{x_1}=\dfrac{\omega_2}{x_2}=\dfrac{\omega_3}{x_3}={k}\) |
| 2. | \(\omega_{1}x_{1}=\omega_{2}x_{2}=\omega_{3}x_{3}={k}\) |
| 3. | \(\omega_{1}x_{1}^{2}=\omega_{2}x_{2}^{2}=\omega_{3}x_{3}^{2}={k}\) |
| 4. | \(\omega_{1}^{2}x_{1}=\omega_{2}^{2}x_{2}=\omega_{3}^{2}x_{3}={k}\) |
Four identical solid spheres each of mass 'm' and radius 'a' are placed with their
centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of the square where the axis of rotation is parallel to the plane of the square is :
1.
2.
3.
4.
Shown in the figure is a rigid and uniform one-metre long rod, \(AB\), held in the horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass \(m\) and has another weight of mass \(2m\) hung at a distance of \(75\) cm from \(A\). The tension in the string at \(A\) is:
1. \(2mg\)
2. \(0.5mg\)
3. \(0.75mg\)
4. \(1mg\)
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 |
A uniform circular disc of radius \(50~\text{cm}\) at rest is free to turn about an axis that is perpendicular to its plane and passes through its centre. It is subjected to a torque that produces a constant angular acceleration of \(2.0~\text{rad/s}^2.\) Its net acceleration in \(\text{m/s}^2\) at the end of \(2.0~\text s\) is approximately:
| 1. | \(7\) | 2. | \(6\) |
| 3. | \(3\) | 4. | \(8\) |
The position of a particle is given by \(\vec r = \hat i+2\hat j-\hat k\) and momentum \(\vec P = (3 \hat i + 4\hat j - 2\hat k)\). The angular momentum is perpendicular to:
| 1. | X-axis |
| 2. | Y-axis |
| 3. | Z-axis |
| 4. | Line at equal angles to all the three axes |
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 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. \(12\times 10^{-4}~\text{N-m}\)
1. \(\dfrac{\rho L^3}{8\pi^2}\)
2. \(\dfrac{\rho L^3}{16\pi^2}\)
3. \(\dfrac{5\rho L^3}{16\pi^2}\)
4. \(\dfrac{3\rho L^3}{8\pi^2}\)
