Question

In shown figure , assume pulley is massless and frictionless. Calculate the acceleration of the blocks if blocks are released from rest .

• A. $\frac{m}{M+m}g$
• B. $\frac{M}{M+m}g$
• C. $\frac{M}{m}g$
• D. $\frac{M+m}{M-m}g$
• E. $\frac{M-m}{M+m}g$

Answer 1

Answer: (E)

$\frac{M-m}{M+m}g$

Let the acceleration of the blocks be $a$ and tension in the string be $T$.

Considering the free body diagram of mass $M$,

$Ma=Mg-T$

Considering the free body diagram of mass $m$,

$ma=T-mg$

Solving the two equations gives,

$a=\frac{M-m}{M+m}g$