Question

A cow is tied to a post by a rope. If the cow moves along a circular path, always keeping the rope tight, and describes $88\text{m}$ when it traced out ${72}^{\circ }$ at the centre, then the length of the rope is
$(\pi =\frac{22}{7})$

• A. $74\text{m}$
• B. $35\text{m}$
• C. $70\text{m}$
• D. $72\text{m}$

Answer 1

The correct option is C $70\text{m}$

Let us denote the post by $P$ and let $PA$ be the length of the rope in the tightest position.
Suppose that the cow moves along the arc $AB$ so that $\angle APB={72}^{\circ }$ and arc $AB=88\text{m}$.
Let the length of the wire $PA$ be $r$ metre.

$\theta ={72}^{\circ }=72\times \frac{\pi }{180}=\frac{2\pi }{5}$
We know that,
$l=r\theta$
$\Rightarrow 88=r\times \frac{2\pi }{5}\Rightarrow r=\frac{88\times 5\times 7}{2\times 22}=70\text{m}$