If the body of mass m moving with velocity v its K.E is double then its momentum?
If the body of mass m moving with velocity v its K.E is double then its momentum?
Explanation
Given:
- Initial kinetic energy: KE = ½mv²
- K.E is doubled ⇒ New KE = 2 × ½mv² = mv²
Let initial momentum p = mv
New velocity v' can be found from:
New KE = ½mv'² = mv²
⇒ v'² = 2v²
⇒ v' = √2 × v
So, new momentum = m × v' = m × √2v = √2 × mv = √2 × p
∴ New momentum is √2 times the original.