if momentum of a body increases by 20 percent, then percentage increase in its kinetic energy is...

We know,

KE = ½ mv2

P = mv

Therefore, KE = ½ (mv)2/m = p2/(2m)

Considering the mass to be constant, if the momentum is increased by 20%, let the new momentum be,

P/ = P + 0.2P = 1.2P

The new kinetic energy is, KE/ = (P/)2/(2m)

=> KE/ = (1.12)[P2/(2m)] = 1.44KE

=> (KE/)/KE = 1.44

=> (KE/ - KE)/KE = 0.44

=> (KE/ - KE)/KE × 100% = 44%

  • 117

Momentum
p = m * v


Kinetic Energy
KE = ½ m v²


If you increase momentum by 20% thats the same as saying
1.2 p = m ( 1.2 v)

Thus you are increasing the velocity by 20%

So now you determine how increasing the v by 20% will effect Kinetic Energy.

½m (1.2 v)²

Since 1.2² = 1.44 the Kinetic Energy will increase by 44 %

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