Question

A railway engine is travelling along a circular railway track of radius $1500$ metres with a speed of $66\, km/hr$.
Find the angle turned by the engine in $10$ seconds,

• A. $10^{\circ}$
• B. $7^{\circ}$
• C. $11^{\circ}$
• D. $8^{\circ}$

Answer 1

Answer: (B)

Distance moved by the engine along circular railway track = speed, $\times$ time
$=\left(\frac{66\,km}{1\,hr}\right)\times10\,sec$
$=\frac{66000\,m}{3600\,sec}\times10\,sec =\frac{550}{3}m$
If the angle turned is $\theta$ radians, then
$\theta=\frac{\frac{550}{3}}{1500}=\frac{11}{90}$
$=\frac{11}{90}\times\frac{180^{\circ}}{\pi}$
$=\left(\frac{22}{\pi}\right)^{\circ}=7^{\circ}$