Question

Two bodies of mass 2kg and 3kg have same momentum then K.E are in the ratio of

Answer 1

P=root 2 mK. E.
P^2/2m =K.E
Kinetic energy is inversely proportional to m
Hence ratio 3:2

Answer 2

The ratio of  the Kinetic energy is 3 : 2

Explanation:

Given data

$\text{Mass m}_1 = 2 \ \text{kg}$

$\text{Mass m}_2 = 3 \ \text{kg}$

Both bodies have same same momentum

To find the ratio of the kinetic energy

Same momentum ,

$\text{p}_1 = \text{p}_2$

$\text{m}_1 \text{v}_1 = \text{m}_2\text{v}_2$

$\frac{ \text{m}_2}{\text{m}_1} = \frac{\text{v}_1}{\text{v}_2}$

$\frac{3}{2} = \frac{\text{v}_1}{\text{v}_2}$

$\frac{\text{v}_1}{\text{v}_2} = \frac{3}{2}$

The kinetic energy equation for two bodies are,

$\text{KE} = \frac{1}{2} \text{m}_1\text{v}_1^{2}$

$\text{KE} = \frac{1}{2} \text{m}_2\text{v}_2^{2}$

$\text{Kinetic energy} \frac{\text{K}_1}{\text{K}_2} = \frac{ \frac{1}{2} \text{m}_1\text{v}_1^{2}}{ \frac{1}{2} \text{m}_2\text{v}_2^{2}}$

$\text{Kinetic energy} \ \frac{\text{K}_1}{\text{K}_2} = \frac{ \frac{1}{2} \text{m}_1}{ \frac{1}{2} \text{m}_2} [\frac{ \text{v}_1^{2}}{\text{v}_2^{2}}}]$

$\frac{\text{K}_1}{\text{K}_2} = \frac{ \text{m}_1}{ \text{m}_2} [\frac{ \text{v}_1^{2}}{\text{v}_2^{2}}}]$

Substitute the respective values in above equation

$\frac{\text{K}_1}{\text{K}_2} = \frac{ 2}{ 3} \times [\frac{3^2}{2^{2}}]$

$\frac{\text{K}_1}{\text{K}_2} = \frac{ 2}{ 3} \times [\frac{9}{4}]$

$\frac{\text{K}_1}{\text{K}_2} = \frac{ 3}{ 2}$

In terms of ratio,

$\text{K}_1 : {\text{K}_2} = 3 : 2$

Therefore, the ratio of kinetic energy of two bodies of mass 2 kg and 3 kg have same momentum is 3 : 2

To Learn More

1) 2 bodies of masses 3kg and 5kg have the same momentum . Find out the ratios of their kinetic energies . Which one has a larger kinetic energy

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2) Two bodies of mass 1kg and 4kg have equal kinetic energy.what is the ratio of their momentum?

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