Blocks of mass `M_(1)` and `M_(2)` are connected by a cord which passes over the pulleys `P_(1)` and `P_(2)` as shown in the figure. If there is no friction, the acceleration of the block of mass `M_(2)` will be

Options

A. `(M_(2)g)/((4M_(1)+M_(2)))`
B. `(2M_(2)g)/((4M_(1)+M_(2)))`
C. `(2M_(1)g)/((M_(1)+4M_(2)))`
D. `(2M_(1)g)/((M_(1)+M_(2)))`

Answer

A

Explanation

`M_(1)a_(1)=T,M_(2)g-2T=M_(2)a_(2),a_(1)=2a_(2)`
Hence `M_(1)(2a_(2))=T` and `M_(2)g-2M_(1)(2a_(2))=M_(2)a_(2)`
`M_(2)g=a_(2)(4M_(1)+M_(2))` so `a_(2) =(M_(2)g)/(4M_(1)+M_(2))`