A block of mass m is attached with a massless spring of force constant k. The block is placed over a rough inclined surface for which the coefficient of friction is `mu=(3)/(4)`. The minimum value of M required to move the block up the plane is (Neglect mass of string, mass of pulley and friction in pulley)

Options

A. `m//2`
B. `m//3`
C. `m//4`
D. None of these

Answer

a

Explanation

Let `m` start moving down and extension produced in spring be x at any time Value of x required to move the block `m`is

`kx = mu mg cos theta + mg sin theta`
`rArr kx = 0.5 mg (4)/(5)+ mg (3)/(5) = mg`
For minimum `M` is will stop after producing extension in the spring x
`Mgx = (1)/(2) kx^(2) rArr Mg = (1)/(2)kx`
`rArr Mg = (1)/(2) mg rArr M = (m)/(2)`