A uniform of rope length `L` and mass `M` is placed on a smooth fixed wedge as shown. Both ends of rope are at same horizontal level. The rope is initially released from rest, then the magnitude of initial acceleration of rope is.

Options

A. zero
B. `(cos alpha-cos beta) g`
C. `(tan alpha-tan beta) g`
D. `(cosec alpha-cosec beta)g`

Answer

A

Explanation

Let `L_(1)` and `L_(2)` be the portions ( of length) or rope on left and right surface of wedge as shown
`:.` magnitude of acceleration of rope
`a=M/L([L_(1) sin alpha-L_(2) sin beta]g)/M=0` (`:. L_(1) sin alpha=L_(2) sin beta`)