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A body of mass m=10^(-2) kg is moving in...

A body of mass m=`10^(-2)` kg is moving in a medium and experiences a frictional force `F =-kv^2`. Its initial speed is `v_0=10m*s^(-1)`. If after 10 s ,its energy is
`1/8 mv_0^2` , the value of k will be

A

`10^(-3)kg*m^(-1)`

B

`10^(-3)kg*s^(-1)`

C

`10^(-4)kg*m^(-1)`

D

`10^(-1)kg*m^(-1)*s^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(K_f)/(k_i)=(1/8mv_0^2)/(1/2mv_0^2) or,(1/2mv_f^2)/(1/2mv_0^2)=1/4`
`or, (v_f)/(v_0)=1/2 or, v_f=(v_0)/2 =(10)/(2)=5m*s^(-1)`
Given , F `=-kv^2`
Also, `(dv)/(dt)=F/m=(-kv^2)/(m)`
`therefore int_(v_0=10)^(v_f=5)=(dv)/(v^2)=-k/m""int_(t=0)^(t=10)dt`
`or, [-1/v]_(10)^(5)=-k/m""[t]_0^(10) or, -1/(10)=-k/mxx10`
`or, k=10^(-4)kg*m^(-1)`
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