A block mass `m = 2 kg` is moving with velocity`v_(0)` towards a massless unstretched spring of the force constant `k = 10 N//m`. Coefficient of friction between the block and the ground is `mu = 0.2`. Find the maximum value of `v_(0)` so that after pressing the spring the block does not return back but stops there permanently.

Options

A. `2 sqrt((2)/(5)) m//s`
B. `sqrt((1)/(5)) m//s`
C. `4 sqrt((1)/(5)) m//s`
D. `4 sqrt((2)/(5)) m//s`

Answer

D

Explanation

Block will stop there if `kx = mu mg implies x = (mu mg)/(k)`
` implies x = (0.2 xx 2 xx 10)/(10) = (2)/(5) m`
Now using energy conservation
`(mv^(2))/(2) = (kx^(2))/(2) + mu mg (x+1) implies v = 4 sqrt((2)/(5)) m//s`