Question

A block is placed on a plank, which is placed on a horizontal plane. A massless but elastic string deviates by an angle $\theta$ with vertical when a force $F$ is applied to the plank to shift it to the right making the block slide over it. If $F_P$ and $F_B$ are frictional forces between plank and plane and between block and plane, respectively, then work done by the applied force is given by :

• A. work done against friction acting on plank $+$ energy in the elastic string due to work done by friction acting on block.
• B. work done against frictions acting on plank and block $+$ energy in the elastic string.
• C. energy in the elastic string.
• D. difference of work done against frictions acting on plank and block.

Answer 1

The correct option is A work done against friction acting on plank $+$ energy in the elastic string due to work done by friction acting on block.

When a plank is moved, the string is under tension. Work done by force $F$ tries to neutralise the frictional force of plank($F_P$) and elongation of the string due to non-sliding of the block due to its friction($F_B$).
Hence, work done by $F$ will be equal to work done against friction acting on plank $+$ energy in the elastic string due to work done by friction acting on block.