Question

Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to block of mass M as shown in the figure. The magnitude of force P is:

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

Answer 1

Answer: (A)

Acceleration of the system: $a=\frac{P}{M+m} \ldots(1)$
The $FBD$ of mass $m$ is shown

$R\,sin\,\beta=ma\ldots (2)$
$R\,cos\,\beta= mg \ldots(3)$
From (2) and (3)
$A=g \,tan\,\beta$
Putting the value of a in (1), we get
$P=(M+m)g\,tan\,\beta$