Two bodies of masses `m` and `4m` are attached to a light string as shown in figure. A body of mass m hanging from string is executing oscillations with angular amplitude `60^@`, while other body is at rest on a horizontal surface. The minimum coefficient of friction between mass `4m` and the horizontal surface is (here pulley is light and smooth)

Options

A. `(1)/(4)`
B. `(1)/(3)`
C. `(1)/(2)`
D. `(2)/(3)`

Answer

C

Explanation

`h=l(1-cos 60^(@))=(1)/(2),v^(2)=2gl=gl`
Now, `T_(max)-mg=(mv^(2))/(l)("at bottommost point")`
`therefore" "T_(max)=2mg=mu_(s)(4mg)`
`therefore" "mu_(s)=0.5`