A uniform sphere of weight W and radius 5, cm is being held by a string as shown in figure. tension

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4-1.Newton's Laws of Motion

hard

A uniform sphere of weight $W$ and radius $5\, cm$ is being held by a string as shown in the figure. The tension in the string will be

$\frac{12}{5}\,W$

$\frac{5}{12}\,W$

$\frac{13}{5}\,W$

$\frac{13}{12}\,W$

(JEE MAIN-2013)

Solution

$\begin{array}{l}
PQ = \sqrt {O{P^2} + O{Q^2}} \\
= \sqrt {{{13}^2} + {5^2}} = 12\\
Tension\,in\,the\,string\,T,\,so,\,T\cos \theta = w\\
\Rightarrow T = \frac{w}{{\cos \theta }} = \frac{{13}}{{12}}W
\end{array}$

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Solution

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