Question

Two masses of 1g and 4g moving with equal kinetic energies. Then find the ratio of the magnitude of their momentum.

Answer 1

K.E.1 = K.E.2. ( given)

P^2/2m1 = P^2/2m2 {K.E. = P^2/ 2}

Putting M1 = 1 and M2 = 4

P1^2/2×1 =P2^2/2×4

P^12/2 = P2^2/8

P1^2/P2^2 = 2/8

P1/P2 =√1/√4

P1/P2 = 1/2

Thus, the ratio is 1:2.

By Sonam Tyagi

Answer 2

ANS-KE= 1/2 m*v^2

Momentum (p)=m*v

Set each of the 1 gram and 4 grams KE to 8:

KE=1/2 *1* (4)^2=8

KE=1/2 *4* (2)^2=8

The 1 gram takes 4 m/s to achieve KE of 8.

The 4 gram takes 2 m/s to achieve KE of 8.

Therefore, the ratio of their linear momentum (m*v) is:

1*4/4*2= 4/8= 1/2