A block of mass m is connected to a spring of force constant k. Initially the block is at rest and the spring has natural length. A constant force F is applied hrizontally towards right. The maximum speed of the block will be (there is no friction between block and the surface)

Options

A. ` (F)/(sqrt(2mgk))`
B. ` (F)/(sqrt(mk))`
C. ` (sqrt(2)F)/(sqrt(mk))`
D. ` (2F)/(sqrt(mk))`

Answer

B

Explanation

Maximum speed is at equilibrium where
`F=kx rArr x=F/k`
Now, `F.x=1/2mv^(2) + 1/2kx^(2)`
or `F(F/k) =1/2mv^(2) + 1/2 k(Fk)^(2)`
Solving we get,
`v=F/(sqrt(mk)) =v_(max)`.