A uniform rod of length \(200~ \text{cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium? (Take \(g=10~( \text {m/s}^2)\)
1. | \({\dfrac 1 6}~\text{kg}\) | 2. | \({\dfrac 1 {12}}~ \text{kg}\) |
3. | \({\dfrac 1 2}~ \text{kg}\) | 4. | \({\dfrac 1 3}~ \text{kg}\) |
What would be the torque about the origin when a force \(3\hat{j}\) N acts on a particle whose position vector is \(2\hat{k}\) m?
1. | \(6\hat{j}\) N-m | 2. | \(-6\hat{i}\) N-m |
3. | \(6\hat{k}\) N-m | 4. | \(6\hat{i}\) N-m |
A solid cylinder of mass \(2\) kg and radius \(4\) cm is rotating about its axis at the rate of \(3\) rpm. The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6\) N-m
2. \(2\times 10^{-6}\) N-m
3. \(2\times 10^{-3}\) N-m
4. \(12\times 10^{-4}\) N-m