Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEETPhysicsCenter of Mass, Momentum and Collision

A projectile of mass M is fired from the ground with an initial speed u at an angle of 60^ to the horizontal. At the highest point of its trajectory, it explodes into two fragments of mass M 3 and 2M 3 . If the lighter fragment comes to rest immediately after the explosion, the extra energy released during the explosion is

Options

  1. AM u^2 4
  2. B3 M u^2 16
  3. CM u^2 16
  4. DM u^2 8

Correct answer

C. M u^2 16

Step-by-step solution

At the highest point of the trajectory, the vertical component of velocity is zero. The horizontal component of velocity is: v_x = u 60^ = u 2 The kinetic energy of the projectile just before the explosion is: K_i = 1 2 M ( u 2 )^2 = M u^2 8 The momentum of the projectile just before the explosion is entirely horizontal: p_i = M ( u 2 ) = M u 2 Let v_f be the velocity of the heavier fragment (mass 2M 3 ) after the explosion. Since the lighter fragment (mass M 3 ) comes to rest, its momentum is zero. By conservation

Practice Center of Mass, Momentum and Collision on Quantrex Academy →

More from Center of Mass, Momentum and Collision

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two point particles of unit mass start moving simultaneously from point A ( = 2 ) with identical unifo 2026Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of length 10 m, as shown in the figure. Point mass A of mass m travelling horizontally with spe 2026A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and rises to a height of 10 m . The impulse imparted to the ball during its collision with the gro 2025Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v₁ while body B is at rest before collision. The velocity of 2024Two particles A and B initially at rest, move towards each other under mutual force of attraction. At an instance when the speed of A is v and speed of B is 3 v , the speed of cent 2023A 1 ~kg object strikes a wall with velocity 1 ~ms ⁻¹ at an angle of 60^ with the wall and reflects at the same angle. If it remains in contact with wall for 0.1 ~s , then the force 2023A bullet of mass m hits a block of mass M elastically. The transfer of energy is the maximum, when 2023A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1 . If the fragments having equal mass fly off along mutually perpendicula 2022 Full Center of Mass, Momentum and Collision list All NEET PYQs