An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 sec. What is the angular speed and linear speed of motion? (1) 0.11 rad/s, 3.28 cm/s (2) 0.40 rad/s, 5 cm/s (3) 0.44 rad/s, 5.28 cm/s (4) None of these

Answer: (3) 0.44 rad/s, 5.28 cm/s

  • Circular groove of radius = 12 cm
  • Insects completes 7 revolutions in 100 sec

The time period of revolution can be calculated as

T = 100/7 sec

Angular speed

We can calculate the angular speed using this time period formula as

\(\begin{array}{l}omega = frac{2pi }{T}\end{array} \)

\(\begin{array}{l}omega = frac{2times frac{22}{7} }{frac{100}{7}}\end{array} \)

ω = 0.44 rad/sec

Linear speed

We can calculate the linear speed using the formula

Linear speed = rω

Linear speed = 12 × 0.44

Linear speed = 5.28 cm/sec

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