As shown, there is no friction between horizontal surface and the lower block `(M = 3 kg)`. But friction coefficient between both the block is `0.2`. Both the blocks move together with initial speed v towards the spring of force constant `k = 400 N//m` and compresses it. What can be the maximum valure of v, so that during the notion there is no slipping between the blocks ?

Options

A. `20 cm//s`
B. `10 cm//s`
C. `30 cm//s`
D. `40 cm//s`

Answer

A

Explanation

`(1)/(2) (M + m)v^(2) = (1)/(2) kxm^(2)`
`x_(m) = sqrt(((M + m)v^(2))/(k))`
Now for upper block `a_(M) = (kx)/(M + m)`
`mu mg ge (kx_(m) m)/(M + m)`
So for limiting values `v = mu g sqrt((M + m)/(k))`
`V_("max") = 20 cm//s`