Question

In figure, a body A of mass m slides on plane inclined at angle θ₁ to the horizontal and µ₁ 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 angle θ₂ to the horizontal. Which of the following statements are true?

1. A will never move up the plane.
2. A will just start moving up the plane when `µ = (sin  θ_2 - sin  θ_1)/(cos  θ_1)`
3. For A to move up the plane, θ₂ must always be greater than θ₁.
4. B will always slide down with constant speed.

Answer 1

b and c

Explanation:

This system can be represented by the figure given below.

Here we have `f = μmg  cos θ_1`

Now, body A will move up and body B will move down the plane,

If `mg  sin θ_1  +  f = mg  sin θ_2`

That gives us, `mg  sin θ_1  +  μmg  cos θ_1 = mg  sin θ_2`

Or, `μ  cos θ_1 = sin θ_2  -  sin θ_1`

Hence, `μ = s (hati nθ_2 - sin θ_1)/(cos θ_1)`

 Also, body A will move down and body B will move up the plane,

If `mg  sin θ_2  -  mg  sin θ_1 > 0`

Or, `sin θ_2 > sin θ_1`

Hence, θ₂ > θ₁.