Question

Find the force exerted at the support $S$ in terms of ‘$m$’ if the system shown is in equilibrium.

• A. $3\text{mg}$
• B. $2\text{mg}$
• C. $4\text{mg}$
• D. $5\text{mg}$

Answer 1

The correct option is C $4\text{mg}$

FBDs of both pulleys and the body of mass $m$ is as shown

Let the force exerted at the support $S$ is $F$
Then, from the equilibrium condition we have,
From pulley 1, $F=2T$
From pulley 2, $T=2T^{{}^{\prime }}$
And, from the body of mass $m$, $T^{{}^{\prime }}=mg$
So, from above equations we have
$F=2T=2\left(2T{}^{\prime }\right)=4T{}^{\prime }=4mg$