Two blocks `A` and `B` of masses `m=10kg` and `M=20kg` respectively are planed on each other and their combination rests on a fixed horizontal surface `C` . A light string passing over the smooth light pulley is used to contact `A` and `B` as shown. The coefficient of sliding friction between all surface in contact is `mu=(1)/(4)` . if `A` is dragged with a force `F` then for both `A` and `B` to move with a uniform speed we have.

Options

A. `175N`
B. `100N`
C. `125N`
D. None of these

Answer

A

Explanation

For `A` : `F=T+f_(1)+f_(2)`
`F=T+mum_(B)g+mu(m_(A)+m_(B))g`
`F=T+mu(m_(A)+2m_(B))g` (i)
For `B` : `T=f_(1)=mum_(B)g` (ii)
From (i) and (ii) `F=mu(3muM+m_(A))g`
`=(1)/(4)(3xx20xx10)10`
`=(1)/(4)(60+10)xx10=175N` .