Question

two particle with equal kinetic energies are having masses in the ratio of 1/2 . then linear momenta will be in the ratio.
ans-0.707​

Answer 1

Explanation:

KE=p²/2m

KE1/KE2=p1²/p2²Xm2/m1

p1/p2=√m1/m2

p1/p2=1/√2

Answer 2

Ratio of the linear momentum is $\dfrac{p_1}{p_2}=0.707$

Explanation:

Let $m_1\ and\ m_2$ are masses of two objects and $K_1\ and\ K_2$ are their kinetic energy. The relationship between the kinetic energy and the momentum is given by :

$K_1=\dfrac{p_1^2}{2m_1}$

Let K' is the new kinetic energy. It is given by :

$K_2=\dfrac{p_2^2}{2m_2}$

Given, $\dfrac{m_1}{m_2}=\dfrac{1}{2}$

$p^2_1=2K_1m_1$................(1)

$p^2_2=2K_2m_2$.............(2)

Since, two particles have same kinetic energy. So,

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

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

$(\dfrac{p_1}{p_2})^2=\dfrac{1}{2}$

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

$\dfrac{p_1}{p_2}=0.707$

So, the ratio of kinetic energy is 0.707:1. Hence, this is required solution.

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Topic : Linear momentum

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