Question

A block A is placed over a long rough plank B of same mass as shown in figure. The plank is placed over a smooth horizontal surface. At time t = 0, block A is given a velocity v₀ in horizontal direction. Let v₁ and v₂ be the velocities of A and B at time t. Then choose the correct graph between v₁ or v₂ and t :

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Answer 2

Friction force between A and B (= µmg) will accelerate B and retard A till slipping is stopped between the two and since mass of both are equal.

acceleration of B = retardation of A = µg

\ v₁ = v₀ – µgt and v₂ = µgt

Hence, the correct graph is (2). After slipping is ceased the common velocity of both will become $\frac { \mathrm { v } _ { 0 } } { 2 }$ , which can be obtained from conservation of linear momentum also.