Question

2 lead Sphears have radii in the ratio 1 : 2 and have the same linear momentum.What is the ratio of their kinetic energy?

Answer 1

Answer:

KE = 1/2mv^2

p = mv

KE = (p^2)/2m

Since they have same 'p'

We can write

KE1:KE2 = m2:m1

Mass is directly proportional to the volume

m ∝ r^3

m2:m1 = (r2 : r1) ^3 = (2:1)^3 = 8:1

as KE1:KE2 = m2:m1 = 8:1

KE1:KE2 = 8:1