A body of mass m = 1 kg is moving in a medium and experiences a frictional force F = - k v , where v is the speed of the body. The initial speed is v 0 = 10 m s - 1 and after 10 s, its energy becomes half of the initial energy. Then, the value of k is

Question

A body of mass m = 1 kg is moving in a medium and experiences a frictional force F = - k v , where v is the speed of the body. The initial speed is v 0 = 10 m s - 1 and after 10 s, its energy becomes half of the initial energy. Then, the value of k is, 10 ln 2, ln 2, 1 20 ln 2, 10 ln 2

MARKS App · Accepted Answer

∵ According to the question, 1 2 m v f 2 = 1 2 × 1 2 m v i 2 v i , v f = i n i t i a l a n d f i n a l s p e e d s o f t h e b o d y or v f 2 = v i 2 2 or v f = 10 2 Given, F = - k v or m a = - k v ⇒ m d v d t = - k v ⇒ ∫ 10 10 2 1 v d v = - ∫ 0 10 k d t ∵ m = 1 k g ⇒ l n v 10 10 2 = - k 10 ⇒ l n 10 2 - l n 10 = - k 10 ⇒ k = 1 10 l n 10 10 2 = 1 10 l n 2 = ln ⁡ 2 20

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