Q. Block B of mass 100 kg rests on a rough surface of friction coefficient `mu = 1/3.` A rope is tied to block B as shown in figure.The maximum acceleration with which boy A of 25 kg can climb on rope without making body move is:
When the boy climbs up he exerts a tension on the rope. On the rope (at the side of the boy) will have to forces acting on it. They are tension(T) and the weight of boy (25g).
On the other side when the horizontal component of the tension exceeds the limiting friction(F) of the block B it will start to move.
`F = muR`
`F = 1/3xx100xxg = (100g)/3`
At the critical state;
`Tcos37 = F`
`T = (100g)/(3cos37)`
For the climbing of boy using F = ma
`T-25g = 25a`
`a = (T-25g)/(25)`
`a = ((100g)/(3cos37)-25g)/25`
`a = 0.6695g`
`a cong g/3`
So the most suitable answer is B).