An arrangement of the masses and pulleys is shown in the figure. Strings connecting masses `A` and `B` with pulley are horizontal and all pulleys and strings are light. Friction coefficient between the surface and the block `B` is `0.2` and between block `A` and `B` is `0.7`. The system is released from rest. (use `g=10m//s^(2))`

Options

A. The magnitude of acceleration of the system is `2m//s^(2)` and there is no slipping between block `A` and block `B`.
B. The magnitude of friction force between block `A` and block` B` is `42N`
C. Acceleration of block `C` is `1m//s^(2)` downwards.
D. Tension in the string connecting block `B` and block `D` is `12N`.

Answer

A, D

Explanation

Suppose block `A` and `B` move together. Applying `NLM` on `C,A+B,` and `D`
`60-18-T'=9a`
`T'-10=1a`
Solving `a=2m//s^(2)`
To check slipping between `A` and `B` , we have to find friction force in this case. If it is less than limiting static friction, then there will be no slipping between `A` and `B`. ltbr. Applying `NLM` on `A`.
`T-g=6(2)`
as `T=48N`
`f=36N`
and `f_(s)=42N` hence `A` and `B` move together.
and `T'=12N`.