question_answer

Two blocks of masses M and m are connected with either end of a massless string which pass over a smooth pulley\[(M>m)\]. The pulley is connected with the roof of an elevator moving with acceleration 'a' upwards. The relative acceleration of block M relative to block m is 2a. Ratio \[\frac{M}{m}\] is:

A)  \[1+\frac{a}{g}\]                             

B)  \[1-\frac{a}{g}\]

C)  \[1+\frac{2a}{g}\]                          

D)  \[1-\frac{2a}{g}\]

Correct Answer: C

Solution :

Relative acceleration of M relative to m             \[=2a=a(-a)\] In lift frame since, M > m, M is moving downward with acceleration a.             \[M(g+a)\,-T=Ma\]             Or        \[T=Mg\]             Or        \[T-ma\,-mg=ma\]                         \[T=m(2a+g)\]             Comparing \[Mg=m\,(2a+g)\]                         \[\frac{M}{m}\,=\frac{2a+g}{g}=1+\frac{2a}{g}\]