If ke of a body increases by 0.1 the percentage increase in its momentum will be?

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Answer 1 · 2018-03-29T06:14:36

The increase in momentum is #=0.05#

The kinetic energy is #E=1/2mv^2#

The momentum is is #p=mv#

#v=sqrt((2E)/m)#

Therefore,

#p=mv=msqrt((2E)/m)=sqrt(2mE)#

Taking logs

#lnp=1/2(ln2+lnm+lnE)#

Differentiating

#(Deltap)/p=1/2((Deltam)/m)+1/2((DeltaE)/E)#

But,

#(DeltaE)/E=0.1#

Therefore,

#(Deltap)/p=1/2*0.1=0.05#