A block of mass `1 kg` moves towards a spring of force constant `10 N//m`. The spring is massless and unstretched. The coeffcient of friction between block and surface is `0.30`. After compressing the spring, block does not return back : `(g = 10 m//s)`.

Options

A. the maximum value of speed of block for which it is possible is `3.8 m//s`
B. the maximum value of speed of block of which it is possible is `4.2 m//s`
C. if `E_(i)` and `E_(f)` are initial and final mechanical energy, which is sum of kinetic energy and potential energy, than work done by friction on a system is `(E_(i) - E_(f))`.
D. statement in option `( C)` is wrong.

Answer

A, C

Explanation

The spring is compressed by `x`
Block will not return if `mu mg ge Kx`
So, `x_(max) = (mu mg)/(K) =((0.3)(1)(10))/(10) =0.30 m`
work done against friction `= E_(i) - E_(f)`
`mu mg(x+2)=(1)/(2) mv_(0)^(2) -(1)/(2) Kx^(2)`
`(0.3)(1)(10)(0.3+2)=((1)/(2))(1) v_(0)^(2) -((1)/(2))(10)(0.3)^(2)`
on solving, `v_(0) = 3.8 m//sec`.