Correct Answer - Option 2 : The light body
CONCEPT:
Kinetic energy:
- The energy possessed by a body due to the virtue of its motion is called kinetic energy.
\(\Rightarrow KE=\frac{1}{2}mv^{2}\)
Where KE = kinetic energy, m = mass and v = speed
Linear Momentum:
-
The linear momentum of a body is the quantity of motion contained in the body.
- It is measured in terms of the force required to stop the body in unit time.
- It is also measured as the product of the mass of the body and its velocity i.e.,
⇒ Momentum (P) = mass (m) × velocity (v)
⇒ P = mv
EXPLANATION:
- We know that the kinetic energy of a body is given as,
\(\Rightarrow KE=\frac{1}{2}mv^{2}\) -----(1)
- The linear momentum of a body is given as,
⇒ P = mv -----(2)
By equation 1 and equation 2 the relation between the kinetic energy and the momentum is given as,
\(\Rightarrow KE=\frac{P^2}{2m}\)
If the momentum is constant,
\(\Rightarrow KE\propto\frac{1}{m}\) -----(3)
- By equation 3 it is clear that the kinetic energy is inversely proportional to the mass of the body when the momentum is constant.
- Therefore we can say that the kinetic energy of the light body will be more than the heavy body. Hence, option 2 is correct.
