Question

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 ? .
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 1

Correct Answer - b,c
As is clear from A can move up the plane depending on valuse of `m_(1), m_(2), theta_(1), theta_(2)` and
Friction force `f_(1)`
When `A` just starts moving up the plane `f_(1)` acts down the plane
`:. Mg sin theta_(1) + f_(1) = mg sin theta_(2)`
But `f_(1) = mu R_(1) = mu mg cos theta_(1)`
`:. mg (sin theta_(1) + mu cos theta_(1)) = mg sin theta_(2)`
or `mu cos theta_(1) = sin theta_(2) - sin theta_(1)`
`mu = (sin theta_(2) - sin theta_(1))/(cos theta_(1)`
As `mu` cannot be negative therefore `theta_(2)` must always be greater than `theta_(1)`
.