Question

A train is moving on a circular curve of radius $1500$m at the rate of $66$km per hour. Through what angle has it turned in $10$ seconds?

• A. $\frac{1}{5}$rad
• B. $\frac{11}{45}$rad
• C. $\frac{11}{4}$rad
• D. $\frac{11}{5}$rad

Answer 1

The correct option is B $\frac{11}{45}$rad

Radius of circular curve, $R=1500m$

Speed of trains, $S=66km/hr$

Sonverting speed of train into $m/sec$

Speed of train $=66\times \frac{5}{18}=\frac{110}{3}m/s$

Time travelled, $t=10sec$

Distance converted, $d=s\times t$

$=\frac{110}{3}\times 10=\frac{1100}{3}m$

circumference of circular curve, $C=2\pi R$

$=2\times \frac{22}{7}\times 1500$

$=\frac{66000}{7}m$

As $d<c$, revolutions completed $=0$

Angles turned , $\theta =\frac{d}{c}\times 2\pi$ radians

$=\frac{\left(1100/3\right)}{\left(66000/7\right)}\times 2\times \frac{22}{7}$

$=\frac{44}{180}$ radians

$=\frac{11}{45}$ radians

Angle turned $=\frac{11}{45}$ radians