Question

The momentum of an object is doubled. How does it’s. K.E. change?

CLASS - XI PHYSICS (Work, Energy and Power)

Answer 1

as K.E. = p * p / 2m 
so if momentum of an object gets doubled its kinetic energy becomes 4 times
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Answer 2

K.E. = p² / 2m         where, p ⇒ Momentum ;  m ⇒ Mass
Let the initial K.E. and momentum be K₁ and p₁ respectively and final K.E. and momentum be K₂ and p₂ respectively.
Given: p₂ = 2 (p₁)
From the above formula,
K.E. is directly proportional to p²
So, K₁ / K.₂ = p₁² / p₂²
⇒ K₁ / K₂ = p₁² / (2p₁)² = p₁² / 4×p₁²
⇒K₁ / K₂ = 1 / 4
⇒K₂ = 4(K₁)
Hence, K.E. is quadrupled when its momentum is doubled.