The acceleration of the block B in fig. Assuming the surfaces and the pulley `P_(1)` and `P_(2)` are all smooth, is

Options

A. `F/(4m)`
B. `(3F)/(13m)`
C. `F/(2m)`
D. `(3F)/(17m)`

Answer

B

Explanation

As in fig.

`l_(1)+l_(2)+l_(3)=C`
`l_(1)^(')+l_(2)^(')+l_(3)^(')=0 -V_(B)+V_(B)=V_(B)+V_(A)-V_(B)=0`
`3V_(B)=2V_(A) implies 3a_(B)=2a_(A)`.
Applying Newton's law on A and B,
`F-2T =2 ma_(A), 3T=2ma_(B)`
Solve to get `a_(B)=(3F)/(13m)`.