A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be:

Question

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be: (A) 1: 1 (B) 2: 1 (C) 1: 4 (D) 4: 1

Tardigrade Admin · Accepted Answer

K . E =( P 2/2 m ) K 1=( P 12/2(8)) ; K 2=( P 22/2(2)) K 1= K 2 So, 4 P 22= P 12 ( P 1/ P 2)=2

Q. A body of mass $8 k g$ and another of mass $2 k g$ are moving with equal kinetic energy. The ratio of their respective momenta will be:

$1 : 1$

$2 : 1$

$1 : 4$

$4 : 1$

$K . E = \frac{P ^{2}}{2 m}$
$K_{1} = \frac{P _{1}^{2}}{2 ( 8 )}; K_{2} = \frac{P _{2}^{2}}{2 ( 2 )}$
$K_{1} = K_{2}$
So, $4 P_{2}^{2} = P_{1}^{2}$
$\frac{P _{1}}{P _{2}} = 2$

Q. A body of mass 8kg and another of mass 2kg are moving with equal kinetic energy. The ratio of their respective momenta will be:

1:1

2:1

1:4

4:1