A body of mass `m=10^(-2) kg` is moving in a medium and experiences a frictional force `F=-Kupsilon^(2).` Its initial speed is `upsilon_(0)=10ms^(-2)`. If , after `10s`, its energy is `(1)/(8)m upsilon_(0)^(2)`, the value of `k` will be

Options

A. `10^(-3)" kg m"^(-1)`
B. `10^(-3) " kg s"^(-1)`
C. `10^(-4) " kg m"^(-1)`
D. `10^(-1) " kg m "^(-1)`

Answer

C

Explanation

Given , m = `10^(-2) " kg " v_(0) = 10 `m/s
After t = 10 seconds , final velocity be v .
Given `1/2 mv^(2) = 1/8 mv_(0)^(2)`
`v. = (v_(0))/2 = 10/2 = 5 ` m/s
Frictional force experiences
`F = -kv^(2)`
`m (dv)/(dt) = - kv^(2)`
`int_(v_(0)=10)^(v.=5) (dv)/(v^(2)) = int_(t=0)^(t=10) (-k)/m dt`
`k = 10^(-4) " kg" m^(-1)`