Question

A wedge of mass M = 2m₀ rests on a smooth horizontal plane. A small block of mass m₀ rests over it at left end A as shown in the figure. A sharp impulse is applied on the block, due to which it starts moving to the right with velocity v₀ = 6 m/s. At the highest point of its trajectory, the block collides with a particle of the same mass m₀ moving vertically downwards with velocity v = 2 m/s, and gets stuck with it. If the combined mass lands at the end point A of the body of mass M, the length l is ______ cm. Neglect friction, take g = 10 m/s².

   

विकल्प

• 10.00

• 20.00

• 30.00

• 40.00

Answer 1

A wedge of mass M = 2m₀ rests on a smooth horizontal plane. A small block of mass m₀ rests over it at left end A as shown in the figure. A sharp impulse is applied on the block, due to which it starts moving to the right with velocity v₀ = 6 m/s. At the highest point of its trajectory, the block collides with a particle of the same mass m₀ moving vertically downwards with velocity v = 2 m/s, and gets stuck with it. If the combined mass lands at the end point A of the body of mass M, the length l is 40.00 cm. Neglect friction, take g = 10 m/s².

Explanation:

At the highest point, combined mass velocity is,

H = `20/(2g)` = 1 m

1.2 = 1.T + `1/2` g T²

T = 0.4 sec

u_rel = 1 m/s

⇒ l = u_rel T = 0.4 m

= 40 cm