Question

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

• A. $5w/4$
• B. $15w/4$
• C. $15w/16$
• D. None of these

Answer 1

The correct option is A $5w/4$

By the free body diagram


$\cos \theta =\frac{3}{5}$

$\sin \theta =\frac{4}{5}$
As sphere is at equilibrium,
$T\sin \theta =w$
$T\left(\frac{4}{5}\right)=w$
$T=\frac{5w}{4}$

Hence, the option A is the correct option.