Two wooden blocks of masses $M$ and $m$ are placed on a smooth horizontal surface as shown in figure. If a force $P$ is applied to the system as shown in figure such that the mass $m$ remains stationary with respect to block of mass $M$, then the magnitude of the force $P$ is

• Correct answer
  A

  $(M+m) g \tan \beta$
• B

  $g \tan \beta$
• C

  $m g \cos \beta$
• D

  $(M+m) g \operatorname{cosec} \beta$

Solution

The free body diagram of the given situation is
$\begin{aligned} & \text { Force }=\text { Mass } \times \text { Acceleration } \\ & \therefore \quad P=(M+m) a \\ & m a \cos \beta=m g \sin \beta \\ & \Rightarrow \quad a=g \frac{\sin \beta}{\cos \beta} \\ & =g \tan \beta \\ & \therefore \quad P=(M+m) g \tan \beta \\ & \end{aligned}$

Hence, the correct answer is option: 'A'.