A body of mass m = 10-2 kg is moving in a medium and experiences a frictional force F = -kv2. Its initial speed is v0 = 10m-1. After 10s, if its energy is 0.125 mv02 the value of k will be

dvdt=−100kv2∫dv−100kv2=∫0dt1100k×1v=1100k[15−110]

A body of mass m = 10-2 kg is moving in a medium and experiences a frictional force F = -kv2. Its initial speed is v0 = 10m-1. After 10s, if its energy is 0.125 mv02 the value of k will be

dvdt=−100kv2∫dv−100kv2=∫0dt1100k×1v=1100k[15−110]

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A body of mass m = 10^-2 kg is moving in a medium and experiences a frictional force F = -kv². Its initial speed is v₀ = 10m^-1. After 10s, if its energy is 0.125 $m v_{0}^{2}$ the value of k will be

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$10^{- 4} {kgm}^{- 1}$

$10^{- 1} {kgm}^{- 1} s^{- 1}$

$10^{- 3} {kgs}^{- 1}$

$10^{- 3} {kgm}^{- 1}$

answer is D.

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$\frac{d v}{d t} = - 100 k v^{2}$

$\int \frac{d v}{- 100 k v^{2}} = \int_{0}^{d t} \frac{1}{100 k} \times \frac{1}{v} = \frac{1}{100 k} [\frac{1}{5} - \frac{1}{10}]$

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A body of mass m = 10-2 kg is moving in a medium and experiences a frictional force F = -kv2. Its initial speed is v0 = 10m-1. After 10s, if its energy is 0.125 mv02 the value of k will be

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A body of mass m = 10^-2 kg is moving in a medium and experiences a frictional force F = -kv². Its initial speed is v₀ = 10m^-1. After 10s, if its energy is 0.125 $m v_{0}^{2}$ the value of k will be