Study in fig. and answer the following questions accordingly. Neglect all friction and masses of the pulleys.

What is the acceleration of block B?

Options

A. `30//77 ms^(-2)`
B. `60//77 ms^(-2)`
C. `80//77 ms^(-2)`
D. `120//77 ms^(-2)`

Answer

D

Explanation

From constraint relation , we can see that
`2TX_(B)=2TX_(A)`
`X_(A)=3/2 X_(B) implies a_(A) =3/2 a_(B)`
So let `a_(B)=a` then `a_(A)=1.5a`
Writing equation of motion :
From block A,
`2T=70a_(A)=105a = 3 xx 35 a `
`35a = 2/3 T`..(i)
From block B,
`300-3T=35a_(B)=35a` ..(ii)
solving eqs. (i) and (ii) we get
`300-3T=(2T)/(3) implies 900-9T=2T implies 900 = 11T`
`T=(900)/(11)N`
`a_(A)=(180)/(77)ms^(-2) and a_(B) = (120)/(77)ms^(2)`.