Question

A pearl of mass m is in a position to slide over a smooth wire. At the initial instant the pearl is in the middle of the wire. The wire moves linearly in a horizontal plane with an acceleration a in a direction having angle θ with the wire. The acceleration of the pearl with reference to wire is

• A. gsin θ - a cosθ
• B. g sin θ - g cosθ
• C. gsin θ + a cosθ
• D. g cosθ+ a sin θ

Answer 1

Answer: (A)

gsin θ - a cosθ

Answer 2

Let a_x, a_y and a_r be the net leftward horizontal acceleration bead, net downward vertical acceleration of bead and relative acceleration of bead with reference to rod respectively. Then

a_y = a_r cos θ + a

and a_x = a_r sin θ

Projecting forces vertically and horizontally

mg – N cos θ = ma_r + ma cos θ

i.e., a_r = g sin θ - a cos θ