Question bank/JEE Main/Physics

A uniform sphere of weight w and radius 3 m is being held by a
string of length 2 m. attached to a frictionless wall as shown in the
figure. The tension in the string is $\frac{5w}{n}$ then find the value
of n.

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[IMAGE] From geometry:
$\cos\theta = \frac{3}{5}$
$\sin\theta = \frac{4}{5}$
As sphere is at equilibrium
$T\sin\theta = w$
$T\left( \frac{4}{5} \right) = w$
$T = \frac{5w}{4}$

Source: Grass-G / P-06 Physics paper 14 October.docx