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)`
`implies " " mg sin theta_(1) + mu mg cos theta_(1) = mg sin theta_(2)`
`implies " " = (sin theta_(2) - sin theta_(1))/(cos theta_(1))`
When A moves upwards
f = mg sin `theta_(2) - mg sin theta_(1) gt 0`
`implies " " sin theta_(2) gt sin theta_(1) implies theta_(2) gt theta_(1)`