Question

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:

• A. $(M+m)g\tan \beta$
• B. $g\tan \beta$
• C. $mg\cos \beta$
• D. $(M+m)gcosec\beta$

Answer 1

The correct option is A $(M+m)g\tan \beta$

Let us take the wedge and block as a system,and assume that the acceleration of this system is $a$.

Then, $P=(M+m)a$.

Now working from the frame of reference of the block of mass $m$,a pseudo force has to be applied on this block.

equation of motion is-

$Ncos\beta =mg$

$Nsin\beta =ma$

dividing these equations we get

$a=gtan\beta$

Also the block has to be at rest with respect to wedge,so it must have same acceleration as the system.

$gtan\beta =\frac{P}{M+m}$

So, required $P$=$(M+m)gtan\beta$.