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Consider the system shown below, with tw...

Consider the system shown below, with two equal masses `m` and a spring with spring constant `K`. The coefficient of friction between the left mass and horizontal table is `mu=1//4`, and the pulley is frictionless. The spring connecting both the blocks is massless and inelastic. The system is held with the spring at its unstretched length and then released.

The minimum value of `mu` for which the system remains at rest once it has stopped for the first time is

A

`(1)/(sqrt(3))`

B

`(1)/(3)`

C

`(1)/(2)`

D

`(1)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
When the masses are stopped at this value of `x`, the forces on left mass for it to remain at rest is zero

`rArr kx=mg+f`
`rArr k(2mg)/(k) (1-mu)lemg+mu mg`
`:. Muge1//3 :. `least value of `mu` is `1//3`.
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