A uniform sphere of weight $W$ and radius $5 \mathrm{~cm}$ is being held by a string as shown in the figure.…

A uniform sphere of weight $W$ and radius $5 \mathrm{~cm}$ is being held by a string as shown in the figure. The tension in the string will be :
  1. $12 \frac{W}{5}$
  2. $5 \frac{W}{12}$
  3. $13 \frac{W}{5}$
  4. $13 \frac{\mathrm{W}}{12}$

Solution


$\begin{aligned} & \mathrm{PQ}=\sqrt{\mathrm{OP}^2+\mathrm{OQ}^2} \\ & =\sqrt{13^2+5^2}=12 \end{aligned}$ Tension in the string $\mathrm{T}$, so, $\mathrm{T} \cos \theta=\mathrm{w}$ $\Rightarrow \mathrm{T}=\frac{\mathrm{w}}{\cos \theta}=\frac{13}{12} \mathrm{~W}$

Asked in: JEE Main 2013 (09 Apr Online)

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