Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main201910 Apr 2019Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Two particles of masses M and 2 M are moving with speeds of 10 m s - 1 and 5 m s - 1 , as shown in the figure. They collide at the origin and after that they move along the indicated directions with speeds v 1 and v 2 , respectively. The values of v 1 and v 2 are, nearly

Options

  1. A6.5 m s - 1 and 3.2 m s - 1
  2. B3.2 m s - 1 and 12.6 m s - 1
  3. C13.02 m s - 1 and 19 . 7 m s - 1
  4. D3.2 m s - 1 and 6.3 m s - 1

Correct answer

C. 13.02 m s - 1 and 19 . 7 m s - 1

Step-by-step solution

From conservation of linear momentum, Along x -axis: 10Mcos30 0 + 5 2M c o s 45 0 = M v 1 c o s 30 0 + 2 M v 2 c o s 45 0 10   M   3 2 +   10 M 1 2 = M 3 2   v 1 + 2 M v 2 1 2 3 2   v 1 + 2 v 2 = 5 ( 3 + 2 ) … (1) Along y -axis: - 10 M 1 2 + 10 M 1 2 = M v 1 1 2 - 2 M v 2 1 2   v 1 2 - 2 v 2 = 5 ( 2 - 1 ) … (2) From equations (1) and (2) v 1 3 2 + 1 2 = 5 3 + 2 + 5 ( 2 - 1 ) v 1 = 13.02   m / s v 2 = 5 3 + 5 2 - 13.02 × 3 2 2 = 19.72   m   s -

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

More from Center of Mass, Momentum and Collision

Two identical bodies A and B of equal masses have initial velocities v₁ = 4 i m/s and v₂ = 4 j m/s respectively. The body A has acceleration a₁ = 6 i + 6 j m/s ^2 while the acceler 2026The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point ( p ) of normal bisector, as shown in the figure is _______. 2026Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at 2026The position of an object having mass 0.1 kg as a function of time t is given as r = (10t^2 i + 5t^3 j ) m. At t = 1 s, which of the following statements are correct ? A. The linea 2026A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2: 2: 3 . The two pieces of equal masses fly off perpendicular to each other 2026In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 ~m / s and 30 ~m / s , respec 2026Given below are two statements : Statement I : For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles. Statement II : Th 2026In a scattering experiment, a particle of mass 2 m collides with another particle of mass m , which is initially at rest. Assuming the collision to be perfectly elastic, the maximu 2025 Full Center of Mass, Momentum and Collision list All JEE Main PYQs