In the arrangement shown in fig., if the acceleration of B is `vec(a)`. Then find the acceleration of A.

Options

A. A) `a sin alpha`
B. B) `a cot theta`
C. C) `a tan theta`
D. D) `a(sin alpha cot theta+cos alpha)`

Answer

D

Explanation

Direction of acceleration of B is along the fixed incline. And that of A is along horizontal towards left. From diagram, accelerations of B is represented by `vec(AB)` while its horizontal and vertical components are shown by AO and OB, respectively. Acceleration of A is represented by `vec(AC)`.
`vec(AC)=a(sin alpha cot theta+cos alpha)`.