Question

If the momentum of a body increases by 0.01 its kinetic energy will increase by

Answer 1

Heya

The relation between momentum (p) and kinetic energy (E) is given as

p = √(2mE)

or

E = p2/2m

now,

as momentum increase by 0.01%, the new momentum will be

p' = p + (0.01/100)p = 1.0001p

so,

the new kinetic energy will be

E' = p^2 / 2m = (1.0001p)2 / 2m

or

E' = 1.0002(p^2/2m) = 1.0002E

thus,

the percentage increase in kinetic energy will be

[(E' - E) / E] x 100

= [(1.0002E - E) / E] x 100

= [1.0002 - 1] x 100

so,

% increase in E = 0.02 %