Question

Find the time period of meeting of minute hand and second hand of a clock?

• A. $60min$
• B. $\frac{59}{60}min$
• C. $\frac{60}{59}min$
• D. $59min$

Answer 1

The correct option is C $\frac{60}{59}min$

${\omega }_{min}=\frac{2\pi }{60}rad/min,{\omega }_{sec}=\frac{2\pi }{1}rad/min$
${\theta }_{sec}-{\theta }_{min}=2\pi$ (for second and minute hand to meet again)
$({\omega }_{sec}-{\omega }_{min})t=2\pi$
$2\pi (1-1/60)t=2\pi \Rightarrow t=\frac{60}{59}min$.
Hence, the time period of the meeting of the minute hand and second hand of a clock is $t=\frac{60}{59}min$.