First slide

Mechanical equilibrium force cases

Question

A uniform sphere of weight W and radius 3 m is being held by a string of length 2m.attached to a frictionless wall as shown in the t figure. The tension in the string will be:

Moderate

A

$\frac{5 W}{4}$
B

$\frac{15 W}{4}$
C

$\frac{15 W}{16}$
D

none of these

Solution

FBD of sphere:
$W = T \sin θ$
and $\cos θ = \frac{3}{5} \Rightarrow θ = 53^{0}$
$\Rightarrow T = \frac{W}{\sin 53^{0}} = \frac{5}{4} W$

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