Question

if angular momentum of a body is increased by 100%.find the percentage change in kinetic energy?

Answer 1

p=√2mKE
p is getting doubled so K2/K1=✓2
hence percentage increase is (✓2 -1)*100=41.4%

Answer 2

Angular momentum (L) and Kinetic energy (K) are related as
K = L^2 / (2 I)

K2 / K1 = (L2 / L1)^2
sqrt(K2 / K1) = (L2 / L1)
sqrt(K2 / K1) - 1 = (L2 / L1) - 1
sqrt(K2 / K1) - 1 = ΔL / L1
sqrt((100 + x) / 100) - 1 = 100/100
sqrt((100 + x) / 100) = 2
(100 + x) / 100 = 4
100 + x = 400
x = 400 - 100
x = 300%

Percentage change in kinetic energy is 300%