First slide

Constraints

Question

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

Moderate

A

$\sqrt{2} Mg$
B

$\sqrt{2} mg$
C

$\sqrt{{(M + m)}^{2} + m^{2} g}$
D

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

Solution

Force on the pulley by the clamp
$F_{pc} = \sqrt{T^{2} + {[(M + m) g]}^{2}}$
$F_{pc} = \sqrt{{(Mg)}^{2} + {[(M + m) g]}^{2}}$
$F_{pc} = g \sqrt{M^{2} + {(M + m)}^{2}}$

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