A string of negligible mass passing over a clamped pulley of mass m supports a body of mass M as shown in figure. The force exerted by the clamp on the pulley is.

Question

A string of negligible mass passing over a clamped pulley of mass m supports a body of mass M as shown in figure. The force exerted by the clamp on the pulley is. (A) g √(M + m)2 + M2  (B) √(M + m)2 + m2 g (C) √2 Mg (D) √2 mg

Tardigrade Admin · Accepted Answer

A free body diagram of a mass pully system is shown below

Now, tension in the string

T - M g = 0

\Rightarrow T = M g

Force in vertical direction,

F_{1} = T + m g

\Rightarrow F_{1} = M g + m g = (M + m) g

Similarly, force in horizontal direction

F_{2} = T = M g

Now, the resultant force

F_{res} = F_{1}^{2} + F_{2}^{2} + 2 F_{1} F_{2} cos 9 0^{\circ}

\Rightarrow F_{res} = F_{1}^{2} + F_{2}^{2} = (M + m)^{2} g^{2} + M^{2} g^{2}

\Rightarrow F_{res} = g (M + m)^{2} + M^{2}

Hence, the resultant force is

g (M + m)^{2} + M^{2}

Q. A string of negligible mass passing over a clamped pulley of mass m supports a body of mass M as shown in figure. The force exerted by the clamp on the pulley is.

$g (M + m)^{2} + M^{2}$

$(M + m)^{2} + m^{2} g$

$2$ Mg

$2$ mg

Q. A string of negligible mass passing over a clamped pulley of mass m supports a body of mass M as shown in figure. The force exerted by the clamp on the pulley is.

g(M+m)2+M2​

(M+m)2+m2​g

2​ Mg

2​ mg

$g (M + m)^{2} + M^{2}$

$(M + m)^{2} + m^{2} g$

$2$ Mg

$2$ mg