Question

When the momentum of a body decreased by 10%,it's KE decreased by
A) 20%
B) 40%
C) 36%
D) None

Answer 1

Option,A for eg suppose your momentum is 10mv and decrease in 10% will give us 9mv
Suppose we had mass = 5kg and According to Newton laws mass has to be constant so the decrease is in the velocity which now becomes 1.8m/s from 2m/s thus now applying kinetic energy
1/2*5*2*2 = 10j (initial energy)
1/2*5*1.8*1.8 = 8.1j final energy after 2nd condition
Thus the whole value decreases by 20%

Answer 2

I think (d) none of these because-

Let the mass is m and the velocity was u

=> momentum =mu

Later the momentum is reduced by 10% i.e. now it is 9/10 mu

Let 9/10 mu= mv

=> v = 9/10 u

=> earlier kinetic energy was 1/2 mu^2 but now it is 1/2 mv^2

=> 1/2 m (9/10u)^2

=> 81/100 (1/2mu^2)

.

%change = 1/2 mu^2 - 81/100 (1/2 mu^2) / 1/2mu^2 ×100

=> 19/100 ×100

=> 19%