A particle of mass m moves on positive x-axis under the influence of force acting towards the origin given by `-kx^2 hat i.` If the particle starts from rest at `x=a,` the speed it will attain when it crosses the origin is

Options

A. `(sqrtk/(ma))`
B. `(sqrt2k/(ma))`
C. `(sqrt(ma)/2k)`
D. None of these

Answer

D

Explanation

`a=F/m=(-kx^2)/m`
`:. v.(dv)/(dx)=-(kx^2)/m`
or `int_0^v vdv=int_a^0-(kx^2)/m dx`
`v^2/2=(ka^3)/(3m)`
`:. v=(2ka^3)/(3m)`