Question

Two bodies of masses 1kg and 4kg have equal kinetic energies the ratio of their momentum is

Answer 1

$k.e. = \frac{ {p}^{2} }{2m}$
${p}^{2} = 2m \times k.e.$

M1 = 1kg
K.E.= x
$p = \sqrt{2x}$

M2= 4kg
K.E. x
$p = \sqrt{8x} = 2 \sqrt{2x}$
Ratio=
$\frac{ \sqrt{2x} }{2 \sqrt{2x} }$
1:2

Answer 2

Answer:

$\dfrac{p_1}{p_2}=\dfrac{1}{2}$

Explanation:

The relationship between the kinetic energy E and the momentum p is given by :

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

For body 1, $E_1=\dfrac{p_1^2}{2m_1}$

For body 2, $E_2=\dfrac{p_2^2}{2m_2}$

Since, the kinetic energies of both bodies are same, so

$\dfrac{p_1^2}{2m_1}=\dfrac{p_2^2}{2m_2}$

$(\dfrac{p_1}{p_2})^2=\dfrac{m_1}{m_2}$

$\dfrac{p_1}{p_2}=\dfrac{1}{2}$

So, the ratio of the momentum of two bodies is 1:2. Hence, this is the required solution.