Question

If momentum of an object is increased by 10 %, then its kinetic energy will increase by

Answer 1

Now, we know K.E.= p²/2m                                                        (original K.E.)
         Now, if Momentum (p) is increased by 10%, new momentum=110p/100

∴ putting new momentum: K.E= (11p/10)²/2m
                                         ⇒K.E.= (121p²/100)/2m                     (new K.E.)
   
∴ Change in K.E. %: 
(difference between new and original K.E./ Original K.E.) · 100
   ⇒ {{[(121p²/100)/2m] - [p²/2m]} /(p²/2m) } · 100
   ⇒ [(21p²/200m)/(p²/2m)] · 100
   ⇒ (21/100) · 100
   ⇒ 21%

∴There is an increase of 21% in Kinetic Energy if momentum is increased by 10%