question_answer

In the figure the block of mass m is at rest on the floor. The acceleration with which a monkey of mass m should climb up along the rope of negligible mass so as to lift the block from the floor is:

A)  \[=\left( \frac{M}{m}-1 \right)g\]      

B)  \[>\left( \frac{M}{m}-1 \right)g\]

C)  \[\frac{M}{m}g\]                            

D)  \[>\frac{M}{m}g\]

Correct Answer: B

Solution :

Equation of motion for M, Since M is stationary             \[T-Mg=0\]                 \[T=Mg\]                             ?.(i) Since, the monkey moves up with an acceleration a             \[T-mg=ma\]                 \[T-m(g+a)\]                      ?..(ii) Equating equations (i) and (ii), we obtain             \[Mg=m(g+a)\]                 \[a=\left( \frac{M}{m}-1 \right)g\] That means, if \[a>\left( \frac{M}{m}-1 \right)g,\] the block M can be lifted from the floor.