Question

A plumb bob of mass $1kg$ is hung form the ceiling of a train compartment. The train moves on a inclined plane with constant velocity. If the angle of incline is ${30}^{\circ }.$ Find the angle made by the string with the normal to the ceiling. Also, find the tension in the string. ($g=10m{s}^2.$ )

• A. ${30}^{\circ },10N$
• B. ${10}^{\circ },30N$
• C. ${10}^{\circ },10N$
• D. ${30}^{\circ },30N$

Answer 1

Answer: (A)

${30}^{\circ },10N$

Refer to the image, here $b=30°$.

It is given that the train moves up the incline at a constant velocity and hence the suspended bob does not experience any pseudo force. ($a=\frac{dv}{dt}=0m{s}^{-2}$)

From the simple geometric analysis, it can be seen that the bob is inclined at an angle of $30°$ with the normal to the ceiling.

The forces acting on the bob are tension in the string $T$ (upward) and the bob’s self-weight $mg$ (downward).

Hence in equilibrium, $T=mg\Rightarrow T=1kg\times g\Rightarrow T=10N$.

Therefore option A is correct.