Correct Answer - Option 1 : √2
Concept:
Momentum
- Momentum is defined as the product of the mass and velocity of the body.
- It is a vector quantity directed toward velocity.
- It is given as
p = mv ----(1)
m is mass, v is the velocity, p is momentum
Kinetic Energy
- The energy of a body in motion due to its state of motion is called kinetic energy.
- It is given as
\(K = \frac{1}{2}mv^2\) ----(2)
K is kinetic energy, m is mass, v is speed.
Relationship between Momentum and Kinetic Energy
If we combine equation (1) and (2) we will get the relationship between momentum and kinetic energy as
\(K = \frac{p^2}{2m}\) ----(3)
Calculation:
If kinetic energy is doubled, then new Kinetic energy K' and new momentum is p'.
K' = 2 K
p' = ?
By the relationship of Kinetic energy and momentum, we can say that
\(K' = \frac{p'^2}{2m}\)
\(\Rightarrow 2K = \frac{p'^2}{2m}\) -- (4)
Putting (3) in (4)
\(\Rightarrow 2\frac{p^2}{2m} = \frac{p'^2}{2m}\)
⇒ 2 p = p'
⇒ p' = √2p
Fractional Change \(\frac{\Delta p}{p} = \frac{p' -p}{p}\)
\(\Rightarrow \frac{\Delta p}{p} = \frac{\sqrt 2 p -p}{p} = \sqrt2 -1\)
