`M_(A) = 3 kg ,M_(B) = 4 kg ,M_(C) = 8 kg`. Coefficient of friction between any two surface is `0.25` pulley is frictionless and string is massless .A is connected to wall through a massless right rod.

Options

A. value of `F` to keep `C` moving with constant speed is `80 N`
B. value of `F` to keep `C` moving with constant speed is `120 N`
C. if `F is 200 N` then acceleration of `B` is `10 m//s^(-2)`
D. to slide `C` towards left ,`F` should be at least ` 50 N` (Take `g = 10m//s^(-2))`

Answer

A, C

Explanation

Maximum value of friction between `A and B` is
`(f_(1))_(max) = 0.25 xx 3 xx 10 = 7.5 N`
Maximum value of friction between `B` and `C`
`(f_(2))_(max) = 0.25 xx 7 xx 10 = 17.5 N`
and maximum value of friction between `C` and ground
`(f_(3))_(max) = 0.25 xx 15 xx 10 = 37.5 N`
`F_(0) =` force on `A` from rod

If `C` is moving with constant velocity, then `B` will also move with constant velocity
For `B, T = 17.5 + 7.5 = 25 N`
For `C, F = 17.5 + 25 + 37.5 = 80 N`
For `F = 200 N`
Acceleration of `B` towards right
`=` Acceleration of `C` towards left
`= a ("say")
Then `T = 7.5 - 17.5 = 4a` ...(i)
`200 - 17.5 - 37.5 - T = 8a` ...(ii)
On solving these two equations, we get
`a = 10 m//s^(2)`