Question

The ratio of the speed of the tip of minute hand to the speed of the tip of the second is:
(Assume same lengths of both hands.)

• A. 1:60
• B. 60:1
• C. 3600:1
• D. 1:3600

Answer 1

The correct option is A 1:60

Let the length of the hands be $R$.

Distance covered by the tip in 1 rotation is equal to the circumference of the circle of radius $R$.
$d=2\pi R$

Time taken by minute hand, $t_1=60min=3600s$
Time taken by second hand, $t_2=60s$

Speed is given by the ratio of distance covered to the time taken. Hence, ratio of speeds of tips minute hand to second hand is:
$\frac{v_1}{v_2}=\frac{d/t_1}{d/t_2}$
$\frac{v_1}{v_2}=\frac{t_2}{d/t_1}$
$\frac{v_1}{v_2}=\frac{60s}{3600s}$
$\frac{v_1}{v_2}=\frac{1}{60}$