A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take π=3.14) :

Solution

Physics sir · 4 steps

Count revolutions first: in 30 minutes the second hand goes round 30 times, the minute hand only half.

1. Count the turns. The second hand makes one full turn every minute, so in 30 minutes it makes 30 revolutions. The minute hand takes 60 minutes for one turn, so in 30 minutes it makes only half a revolution.
2. Second hand tip. One turn covers the circumference 2π r = 2 × 3.14 × 0.75 = 4.71 m. In 30 turns the tip travels 30 × 4.71 = 141.3 m.
3. Minute hand tip. Half a turn covers half the circumference, π r = 3.14 × 0.60 = 1.884 m.

   x = 30(2π)(0.75) - π(0.60) = 141.3 - 1.884 = 139.416 m

4. So. The second hand's tip travels about 139.4 m more, which is option (c).

The idea to keep. For clock hands, distance by the tip is (number of revolutions) times 2π r. Second hand turns once per minute, minute hand once per hour. Always convert the lengths to metres first.

Answer from the NTA final answer key. Solution by PrepWiser.