A body of mass m = 10 − 2 kg is moving in a medium and experiences a frictional force F = − k v 2 . Its initial speed is v 0 = 10 m s − 1 . After 10 s its kinetic energy is 1 8 m v 0 2 , then value of k will be:-

Question

A body of mass m = 10 − 2 kg is moving in a medium and experiences a frictional force F = − k v 2 . Its initial speed is v 0 = 10 m s − 1 . After 10 s its kinetic energy is 1 8 m v 0 2 , then value of k will be:-, 10 − 1 kg m - 1 s - 1, 10 − 3 kg m - 1, 10 − 3 kg s - 1, 10 − 4 kg m - 1

MARKS App · Accepted Answer

After 10 sec, 1 2 m v 2 = 1 8 m v 0 2 ⇒ v = v 0 2 = 5 m s - 1 Acceleration, a = − k v 2 m ⇒ d v d t = − k v 2 m ⇒ ∫ 10 5 d v v 2 = − k m ∫ 0 10 d t - 1 5 + 1 10 = - k 10 - 2 × 10 k = 10 − 4 kg m - 1

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