In a specially designed analog clock, the linear speed of the tip of the minute hand is exactly equal to the linear speed of the tip of the hour hand. The ratio of the length of the minute hand to the length of the hour hand is:

Step-by-step solution

The linear speed v of the tip of a clock hand of length r is given by v = r , where is its angular speed. Given that v_M = v_H , we have: _M r_M = _H r_H r_M r_H = _H _M Since angular speed = 2 T , the ratio becomes: r_M r_H = T_M T_H The time period of the minute hand is T_M = 1 hour. The time period of the hour hand is T_H = 12 hours. Substituting these values: r_M r_H = 1 hour 12 hours = 1 12 Thus, the ratio of the length of the minute hand to the length of the hour hand is 1:12 . Answer: 1:12