What is the largest mass of `C` in `kg` that can be suspended without moving blocks `A` and `B` ? The static coefficent of friction for all plane surface of contact is `0.3` Mass of block `A` is `50 kg` and block `B` is `70 kg`. Neglect friction in the pulleys.

Options

A. `120 kg`
B. `92 kg`
C. `81 kg`
D. None of the above

Answer

C

Explanation

Maximum value of friction between `A` and `B`
`(f_(1))_(max) = mu N_(1) = mum_(A)g`
`= 0.3 xx 50 xx 10`
`= 150 N`
Maximum value of friction between `B` and ground
`(f_(2))_(max) = mu N_(2) = (m_(A) +m_(B)) g`
`= (0.3) (120) (10)= 360 N`
force diagram is as shown below

`T_(2) = (f_(1))_(max) =150 N`
`T_(1) = 2T_(2) + (f_(1))_(max) + (f_(2))_(max)`
`= 300+ 150 + 360 = 810 N`
`T_(1) = m_(c) g`
`:. m_(c) = (T_(1))/(g) = (810)/(10) = 81 kg`