Question

The length of a minute hand of a clock is 4 cm. The average velocity of the tip of the minutes hand when it moves during a time interval from 3 p.m. to 3.45 p.m. is _____ ${ms}^{-1}$.

• A. $2.2\times {10}^{-3}$
• B. 210
• C. $69.7\times {10}^{-5}$
• D. $3.2\times {10}^{-2}$

Answer 1

The correct option is C $69.7\times {10}^{-5}$

The distance moved by tip of minutes hand when it moves during a time interval from 3 p.m. to 3.45 p.m. is $r\theta$

where, r = length of minute hand

$\theta$ = angle moved by minutes hand

$\Rightarrow$ Distance covered $=4\times \frac{3\pi }{2}=6\pi cm$

$\Rightarrow distance=6\pi cm=0.06\pi m$

$\Rightarrow velocity=\frac{distance}{time}$

$\Rightarrow velocity=\frac{0.06\pi }{45\times 60}=69.7\times {10}^{-5}m{s}^{-1}$