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  4. 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

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Q. 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 $P$ isPhysics Question Image

EAMCETEAMCET 2013

Solution:

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