Question

A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60 \,m$, then the magnitude of displacement would be : $\left(\right.$ Given $\left.\cos 135^{\circ}=-0.7\right)$

• A. 42 m
• B. 47 m
• C. 19 m
• D. 40 m

Answer 1

Answer: (B)

$ d = R \theta$
$ 60= R \left(\frac{3 \pi}{4}\right) $
$ R =\frac{60 \times 4}{3 \pi}=\frac{80}{\pi} m $
Displacement $=\sqrt{ R ^2+ R ^2-2 R ^2 \cos 135} $
$ \Rightarrow \sqrt{2 R ^2-2 R ^2(-0.7)}$
$ \Rightarrow \sqrt{3.4 R ^2}=\sqrt{3.4\left(\frac{80}{\pi}\right)^2}$
$\approx 47 m$