Correct Answer - Option 1 : momentum of 1st body > momentum of 2nd body
The correct answer is option 1) i.e. momentum of 1st body > momentum of 2nd body
Kinetic energy (KE): The energy due to the motion of the body is called kinetic energy.
KE = (1/2) m v2
Momentum (p): The product of mass and velocity is called momentum.
p = m v
Where m is mass and v is velocity
K1 = (1/2) m1 v12
K2 = (1/2) m2 v22
The kinetic energies of objects A and B are equal.
K1 = K2
The momenta of objects A and B:
p1 = m1 × v1 and
p2 = m2 × v2
We know that
v1 < v2
Divide the numerator and denominator in the above by K1 and K2 (note K1 = K2), to obtain
v1/K1 < v2/K2
K1/v1 > K2/v2
Substitute K1 and K2 by their expressions given above
(1/2) m1 v12 / v1 > (1/2) m2 v22 /v2
Simplify to obtain
m1v1 > m2 v2
Which gives p1 > p2