A monkey of mass `m` clings a rope to a slung over a fixed pulley .The opposite end of the rope is tried to a weight of mass `M` tying on a horizontal table is `mu` Find the acceleration of weight .The monkey move downward with respect to the rope with an acceleration b.

The acceleration of weight is

Options

A. `(2m(g+b)-mu Mg)/(M +2m)`
B. `(m(g+b)-mu Mg)/(2(M + m)`
C. `(m(g+b)-3mu Mg)/(M +3m)`
D. `(m(g+b)-mu Mg)/(M +2m)`

Answer

d

Explanation

As the monkey move downward with respect to rope with an acceleration b. absulute acceleration is `a+ b`, where a is the acceleration of rope, Therefore equation of motion are
`mg - T = m(a+b)`…(i)
`T - mu Mg = Ma`…(ii)
Putting the value of T from Eqs(ii) and (i) we get
`(m - mu M)g = (M+m)a +mb`
`rArr (m(g - b) - mu Mg)/((M +m))= a`
`T = mu Mg+ (Mmg - Mmb - mu M^(2)g)/(M +m)`
`= (mu M^(2)g + mu Mmg + Mmg - Mmb- mu M^(2)g)/(M +m)`
`= (Mm(mu g +g - b))/(M +m)`