Question

A railway engine is travelling along a circular railway track of radius $1500$ metres with a speed of $66km/hr$.
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
$=\left(\frac{66km}{1hr}\right)\times 10sec$
$=\frac{66000m}{3600sec}\times 10sec=\frac{550}{3}m$
If the angle turned is $\theta$ radians, then
$\theta =\frac{\frac{550}{3}}{1500}=\frac{11}{90}$
$=\frac{11}{90}\times \frac{180^{\circ }}{\pi }$
$={\left(\frac{22}{\pi }\right)}^{\circ }=7^{\circ }$