A body a of mass m slides on plane inclined at angle `theta_(0)` to the horizontal and `mu_(1)` is the coefficient of friction between `A` and the plane `A` is connected by a light string passing over a frictionless pulley to another body `B` also of mass m slidding on a frictionless plane inclined at angle `theta_(2)` to the horizontal Which of the following statements are ture ? .

Options

A. A will never move up the plane.
B. A will just start moving up the plane when `mu =(sin theta_(2)-sin theta_(1))/(cos theta_(1))`
C. For `A` to move up the plane, `theta_(2)` must always be greater than `theta_(1)`.
D. `B` will always slide down with constant speed.

Answer

B, C

Explanation

Let A moves up the plane frictional force on A will be downward as shown.
When A just starts moving up
`mg sin theta_(1) + f =mg sin theta_(2)`
`rArr mg sin theta_(1) + mumg cos theta_(1) = mg sin theta_(2)`
`rArr mu =((sin theta_(2) -sin theta_(1))/(cos theta_1))`
When A moves upwards
`f =mg sin theta_(2), -mg sin theta_(1) gt 0` ltbr gt`rArr sin theta_(2) gt sin theta_(1) rArr theta_(2) gt theta_(1)`
.