First slide

Mechanical equilibrium force cases

Question

Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force F 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 F is

Moderate

A

(M + m)g tanß
B

g tanß
C

mg cosß
D

(M + m)g cosecß

Solution

$\large a = \frac{F}{{M + m}};ma\cos \beta = mg\sin \beta$
$\fn_phv \large \frac{F}{{(M + m)}}\cos \beta = g\sin \beta$
$\large F=(M+m)g tan\beta$

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