The coefficient of static friction between the block of 2 kg and the table shown in figure is `mu_s=0.2.` What should be the maximum value of m so that the blocks do not move? Take `g=10 m/s^2.` The string and the pulley are light and smooth.

Options

A. `2.0kg`
B. `4.0kg`
C. `0.2kg`
D. `0.4kg`

Answer

D

Explanation

Let the mass of the block `B` is `M` .
In equilibrium of block `B` ,
implies `T=Mg` …(i)
If block `A` does not move, then `T=f_(s)`
where `f_(s)` =frictional force `=mu_(S)N=mu_(s)mg`
implies `T=mu_(s)mg` …(ii)
Thus, from Eqs. (i) and (ii), we have
`M=mu_(s)mg` or `M=mu_(s)m`
Given: `mu_(s)=0.2` , `m=2kg`
:. `M=0.2xx2=0.4kg`