Question

Two bodies of mass 2 kg and 3 kg have same momentum then K.E are in
the ratio of
1) 2:3
2 3:2
3) 4:9
4) √2:√3​

Answer 1

Given,

$\sf m_{ \tiny{1}} = 2 \: kg \\ \sf m_{ \tiny{2}} = 3 \: kg \\ \\ \sf Momentum_{ \tiny{1}} = p \\ \sf Momentum_{ \tiny{2}} = p$

We know,

$\bf Momentum = mass \times velocity \\ \\ \tt \longrightarrow 2 v_{ \tiny{1}} = p \\ \tt \longrightarrow3v_{ \tiny{2}} = p \\ \\ \\ \sf v_{ \tiny{1}} = \frac{p}{2} \\ \\ \sf v_{ \tiny{2}} = \frac{p}{3}$

Now,

$\sf \huge E_{ \small{K}} = \frac{1}{2} \times {mv}^{2}$

Therefore,

$\bf \huge Required \: \: Ratio \\ \\ \sf \rightarrow (\frac{1}{2} \times 2 \times \frac{p}{2} ) : ( \frac{1}{2} \times 2 \times \frac{p}{3} ) \\ \\ \sf \rightarrow \frac{ \frac{p}{2} }{ \frac{p}{3} } = \frac{p \times 3}{p \times 2} = \frac{3}{2} \\ \\ \longrightarrow \large \red{3 : 2}$

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Answer 2

The ratio of the kinetic energies of both objects is 3:2.

Explanation:

Given that,

Mass of body 1, $m_1=2\ kg$

Mass of body 2, $m_2=3\ kg$

It is mentioned that both bodies have same momentum. We need to find the ratio of their kinetic energies. The kinetic energy is given by :

$K=\dfrac{p^2}{2m}$

Since, $p_1=p_2$

Taking ratio of kinetic energy of both objects, we get :

$\dfrac{k_1}{k_2}=\dfrac{p^2}{2m_1}\times \dfrac{2m_2}{p^2}$

$\dfrac{k_1}{k_2}=\dfrac{3}{2}$

So, the ratio of the kinetic energies of both objects is 3:2. Hence, this is the required solution.

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Momentum

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