Mass moves on a slope making an angle 9 with the horizontal and is attached to mass `m_(2)` by a string passing over a frictionless pulley . The coefficient of friction between nq and the sloping surface is `mu`. Which of the following statements are true ?

Options

A. If `m_(2) gt m_(1)` sin `theta`, the body will move up the plane
B. If `m_(2) gt m_(1) (sin theta + mu cos theta)`, the body will move up the plane
C. If `m_(2) lt m_(1) (sin theta + mu cos theta)`, the body will move up the plane
D. If `m_(2) lt m_(1) (sin theta - mu cos theta)`, the body will move down the plane

Answer

B, D

Explanation

Assume that mass `m_(1)` move up the plane

Figure shows forces acting on system
N= Normal reaction
F= frictional force
T= Tension in the string
`f = mu N = mu m_(1) g cos theta `
for the sytem `(M_(1) +M_(2))` to move up `M_(2) g - (m_(1) g sin theta + f ) lt 0`
Hence option ( b) is correct
Hence option (d ) is correct