In figure a body A of mass m slides on a plane inclined at angle θ1 to the horizontal and g 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, sliding on a frictionless plane inclined at an angle θ2 to the horizontal.

(a) A will never move up the plane
(b) A will just start moving up the plane when μ=sin θ2sin θ1cos θ1
(c) For A to move up the plane, θ2 must always be greater than θ1
(d) B will always slide down with a constant speed

Which of the following statement/s is/are true?

1. (b, c)
2. (c, d)
3. (a, c)
4. (a, d)

(b, c) Hint: Apply Newton's second law of motion.
Step 1: Find the coefficient of friction.
Let A moves up the plane frictional force on A will be downward as shown.
When A just starts moving up
mg sin θ1+f=mg sin θ2 mg sin θ1+μmg cos θ1=mg sin θ2 μ=sin θ2sin θ1cos θ1
Step 2: Find the friction force.
When A moves upwards
f=mg sin θ2mg sin θ1>0
 sin θ2>sin θ1θ2>θ1