Question

Mass A is released from the top of a frictionless inclined plane 18 m long and reaches the bottom 3s later. At the instant when A is released a second mass B is projected upwards along the plate from the bottom with a certain initial velocity.

Mass B is travels a distance up the plane, stops and returns to the bottom so that it arrives simultaneously with A. The two masses do not collide. Initially velocity of A is

• A. 4 ms^-1
• B. 5 ms^-1
• C. 6 ms^-1
• D. 7ms^-1

Answer 1

Answer: (C)

6 ms^-1

Answer 2

Here for A, 18 = 0 × 3 + 1/2 a × 3² or a = 4 ms^-2 for B, time taken to move up is given by, tl = u/a (∴ the relation v = u + at here becomes 0 = u – at₁). Distance moved up is given by the relation 0 = u² – 2a i.e., S = u²/2a S = 1/2 at²2² and t₂ = $\sqrt{\frac{2S}{a}}$ or t₂ = $\sqrt{\frac{2}{a}\frac{u^{2}}{2a}} = \frac{u}{a}$ But $\frac{u}{a}$ = tl then tl + t2 = 3 or $\frac{2u}{a}$= 3 or u $\frac{3a}{2}$ or u = $\frac{3}{2}$ × 4 = 6 ms^-1