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A block of mass m is attached with a mas...

A block of mass `m` is attached with a massless spring of force constant `k`. The block is placed over a fixed rought inclined surface for which the coefficient of friction is `mu=(3)/(4)` . The block of mass `m` is initially at rest . The block is mass `M` is released from rest with spring in unstretched state. The minimum value of `M` required to move the block up the plane is `(` neglect mass of string and pulley and friction in pulley `)`

A

`(3)/(5)m`

B

`(4)/(5)m`

C

`(6)/(5)m`

D

`(3)/(2)m`

Text Solution

Verified by Experts

The correct Answer is:
A
As long as the block of mass `m` remains stationary, the block of mass `M` released from rest comes down by `(2Mg)/(K)(` before coming it rest momentanly again `)` .
Thus the maximum extension in spring is
`x=(2Mg)/(K) …….(1)`
for block of mass `m` to just move up the incline
`kx=mg sin theta + mu mg cos theta ........(2)`
`2Mg=mgxx(3)/(5)+(3)/(4) mg xx(4)/(5)`
or `M=(3)/(5) m Ans. `
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