Study the following table

Options

A. `(700)/(11)N`
B. `(450)/(11)N`
C. `(500)/(11)N`
D. `(900)/(11)N`

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)`.