Question

A uniform sphere of weight $w$ and radius $3m$ is being held by a string of length $2m$. 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. $Noneofthese$

Answer 1

The correct option is A $5w/4$

For vertical equilibrium

$T\cos \theta =W$

so, Length

$\begin{array}{c}OA=2+3=5m\\ OB=3m\\ \Rightarrow AB=4m\end{array}$

Now, $T\cos \theta =W$

$\begin{array}{c}\Rightarrow T=\frac{W}{\cos \theta }\\ =\frac{W}{\frac{L}{OA}}\\ =\frac{W\times OA}{L}\\ =\frac{W\times 5}{4}\end{array}$

Or, $\frac{5W}{4}$

Hence, Option $A$ is the correct answer. $\frac{5W}{4}$