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JEE Advanced2008PhysicsCenter of Mass, Momentum and CollisionActual

Paragraph: A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60^ to 30^ at point B . The block is initially at rest at A . Assume that collisions between the block and the incline are totally inelastic (g=10 ~m / s ^2 ) Question: The speed of the block at point B immediately after it strikes the second incline is

Options

  1. A60 ~m / s
  2. B45 ~m / s
  3. C30 ~m / s
  4. D15 ~m / s

Correct answer

B. 45 ~m / s

Step-by-step solution

Between A and B , height fallen by block h₁= 3 60^ =3 ~m . speed of block just before striking the second incline, v₁= 2 g h₁ = 2 10 3 = 60 ~ms ⁻¹ In perfectly inelastic collision, component of v₁ perpendicular to B C will become zero, while component of v₁ parallel to B C will remain unchanged. speed of block B immediately after it strikes the incline is, aligned v₂ & = component of v₁ along B C & =v₁ 30^ & =( 60 ) ( 3 2 )= 45 ~ms ⁻¹ aligned correct option is (b)

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