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.