In the figure shown the accelerationof `A` is `a_(A) = (15 hati + 15 hatj)`. Then the acceleration of `B` is (A remain in contact with B)

Options

A. `6 hat(i)`
B. `-15 hat(i)`
C. `10 hat(i)`
D. `-5 hat(i)`

Answer

D

Explanation

Let acceleration of B `vec(a)_(B)=a_(B) hat(i)`
Then acceleration of A w.r.t.
`B=vec(a)_(A)-vec(a)_(R)=(15-a_(B))hat(i)+15 hat(j)`
This acceleration must be along the inclined pplane
so `tan 37^(@)=15/(15-a_(B))rArr 3/4=15/(15-a_(B)) a_(B)=-5`
`rArr vec(a)_(R)=-5hat(i)`