In the arrangement shown in figure, if the acceleration of B is `overline(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, acceleration of B is represented by `vec(AB)` while its horizontal and vertical components are show by AO and OB, respectively. Acceleration of A is represented by `vec(AC) = vec(OA) + vec(OC) = a (sin alpha cot theta + cos alpha)`