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. $(M+m)gtan\beta$
• B. $gtan\beta$
• C. $mgcos\beta$
• D. $(M+m)gcosec\beta$

Answer 1

Answer: (A)

Acceleration of the system: $a=\frac{P}{M+m}\dots (1)$

The $FBD$ of mass $m$ is shown



$Rsin\beta =ma\dots (2)$

$Rcos\beta =mg\dots (3)$

From (2) and (3)

$A=gtan\beta$

Putting the value of a in (1), we get

$P=(M+m)gtan\beta$