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CBSE Class 11-science Answered

IF  LINEAR  MOMENTUM  OF  A  BODY  IS  INCREASED  BY  50%  OF  ITS  INITIAL  VALUE   THEN  WHAT  WILL  BE  THE  %  CHANGE  IN  KINETIC  ENERGY  OF  THE  BODY ?
Asked by pardeepkumar2281 | 26 Sep, 2018, 08:55: PM
answered-by-expert Expert Answer
momentum is increased by 50% means, speed is increased by 50% because mass remains constant.
 
Kinetic Energy E = (1/2)×m×v2 ..................(1)
 
if we differentiate eqn.(1), we get,  dE = (1/2)×m×2v×dv ..........(2)
 
from (1) and (2), we get,  ( dE/E ) = 2×(dv/V)   or  (dE/E)×100 = 2×(dv/V)×100 .................(3)
 
from eqn.(3), we say that percentage change in kinetic energy is twice the percentage change of speed.
 
hence if speed increases by 50%, energy increases by 100%
Answered by Thiyagarajan K | 27 Sep, 2018, 08:23: PM
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