Q. A light particle moving horizontally with a speed of 12 m/s strikes a very heavy block moving in the same direction at 10 m/s.The collision is one-dimensional and elastic. After the...
Q. A light particle moving horizontally with a speed of 12 m/s strikes a very heavy block moving in the same direction at 10 m/s.The collision is one-dimensional and elastic. After the collision,the particle will
A) move at 2m/s in its original direction
B) move at 8m/s in its original direction
C) move at 8m/s opposite to its original direction
D) move at 12 m/s opposite to its original direction
In an elastic collision the kinetic energy is conserved.
When two particles moving along the same axis take part in such collision,
Conservation of momentum requires:
`rArr m_1(v_1-v'_1)=m_2(v_2-v'_2)` --- (i)
Conservation of kinetic energy requires:
`rArr m_1(v_1-v'_1)(v_1+v'_1)=m_2(v_2-v'_2)(v_2+v'_2)` --- (ii)
Dividing by (i) yields:
Assuming the heavier block to be so heavy that its velocity remain unperturbed after the collision with the light patrticle, the final velocity of the light particle (v'_1) can be obtained as:
`rArr v'_1=8` m/s
So, the light particle will move with a velocity of 8 m/s in tha same direction (option B).