A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2 Both of them have the same momentum but their different kinetic energies are E1 and E2 respectively. If m1 m2 , then

Question

A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2 Both of them have the same momentum but their different kinetic energies are E1 and E2 respectively. If m1 > m2 , then (A)  E1 < E2 (B)  ( E1 / E2 ) = ( m1 / m2 )  (C)  E1 > E2 (D)  E1 = E2

Tardigrade Admin · Accepted Answer

Kinetic energy =(p2/2 m) ∴ (E1/E2)=(p12 / 2 m1/p22 / 2 m2) ⇒ (E1/E2)=(m2/m1) text as m1>m2 ∴ E1< E2

Q. A particle of mass $m_{1}$ is moving with a velocity $v_{1}$ and another particle of mass $m_{2}$ is moving with a velocity $v_{2}$ Both of them have the same momentum but their different kinetic energies are $E_{1}$ and $E_{2}$ respectively. If $m_{1} > m_{2}$ , then

$E_{1} < E_{2}$

$\frac{E _{1}}{E _{2}} = \frac{m _{1}}{m _{2}}$

$E_{1} > E_{2}$

$E_{1} = E_{2}$

Kinetic energy $= \frac{p ^{2}}{2 m}$
$∴ \frac{E _{1}}{E _{2}} = \frac{p _{1}^{2} /2 m _{1}}{p _{2}^{2} /2 m _{2}}$
$\Rightarrow \frac{E _{1}}{E _{2}} = \frac{m _{2}}{m _{1}} as m_{1} > m_{2}$
$∴ E_{1} < E_{2}$

Q. A particle of mass m1​ is moving with a velocity v1​ and another particle of mass m2​ is moving with a velocity v2​ Both of them have the same momentum but their different kinetic energies are E1​ and E2​ respectively. If m1​>m2​, then

E1​<E2​

E2​E1​​=m2​m1​​

E1​>E2​

E1​=E2​