A100 kg box sits on an incline held at rest by a very thin rope attached to another mass hanging as shown. the force of friction between the box and the surface is 100 n and the hanging mass=50 kg. determine both of the possible angles of the incline.

If friction is acting along the plane upwards

then in this case we will have

For equilibrium of 100 kg box on inclined plane we have

also for other side of hanging mass we have

now we have

In other case we can assume that friction will act along the plane downwards

so now in that case we will have

also we have

now we have

So the range of angle will be 23.45 degree to 37 degree

d is the correct answer