Question

Two wooden blocks are moving on a smooth horizontal surface such that the mass $m$ remains stationary with respect to the block of mass $M$ as shown. Find the magnitude of $P$.

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

Answer 1

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

Using the concept of pseudo force in the frame of block of mass $M$ we have

Then FBD of $m$ is as shown

Let the system accelerate rightwards with acceleration $a$
Since, $m$ remain at rest w.r.t. $M$ we get from the equation of force as
$mg\sin \beta =ma\cos \beta \Rightarrow a=g\tan \beta$

For the system of $(M+m)$;
$P=(M+m)a$
$=(M+m)g\tan \beta$