In a body A of mass tn slides on plane inclined at angle `theta_(1)`, to the horizontal and p is the coefficent 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, sliding on a frictionless plane inclined at an angle `theta_(2)` to the horizontal. Which of the following statements are true ?

Options

A. a will never move up the plane
B. a will just start moving up the plane when
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

Assume that block A (mass m ) move up along the slope
in this case frictional force will be in downward direction

when A just starts moving up
`mg sin theta _(1) = f = mg sin theta_(2)`
`mu= (sin theta _(2)- sin theta _(1))/( cos theta _(1))`
When A moves upwards
`f= mg sin theta _(2) mg sin theta_(1) lt 0`
`sin theta _(2) lt sin theta_(1) rArr theta _ (2) gt theta_(1)`