Question

Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is:_______.A. 1:9B. 1:3C. 1:1D.3:1E. 9:1

Answer 1

D. 3 : 1

Step-by-step explanation:

Let suppose that A and B are particles. From statement we know that
`K_(A) = K_(B )` (same kinetic energy) and
`m_(A) = 9\cdot m_(B)`. Then,

`K_(A) = K_(B)`

`(1)/(2)\cdot m_(A)\cdot v_(A)^(2) = (1)/(2)\cdot m_(B)\cdot v_(B)^(2)`

`m_(A) \cdot v_(A)^(2) = m_(B)\cdot v_(B)^(2)`

`(v_(B))/(v_(A)) = \sqrt{(m_(A))/(m_(B)) }`

`(v_(B))/(v_(A)) = 3`

And the ratio of the momentum of A to the momentum of B is:

`r = (m_(A)\cdot v_(A))/(m_(B)\cdot v_(B))`

`r = 9* (1)/(3)`

`r = 3`

Hence, the correct answer is D.