A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies E1 /E2 is

Question

A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocities v1 and v2. The ratio of their kinetic energies E1 /E2 is (A) 1 (B)  m1v2/m2v1  (C)  m2/m1  (D)  m1/m2

Tardigrade Admin · Accepted Answer

m1 v1=m2 v2 (conservation of linear momentum) (E1/E2)=((1 / 2) m1 v12/(1 / 2) m2 v22)=(m12 v12/m22 v22) ⋅ (m2/m1)=(m2/m1)

Q. A stationary particle explodes into two particles of masses $m_{1}$ and $m_{2}$ which move in opposite directions with velocities $v_{1}$ and $v_{2}$ . The ratio of their kinetic energies $E_{1} / E_{2}$ is

$1$

$m_{1} v_{2} / m_{2} v_{1}$

$m_{2} / m_{1}$

$m_{1} / m_{2}$

$m_{1} v_{1} = m_{2} v_{2}$ (conservation of linear momentum)
$\frac{E _{1}}{E _{2}} = \frac{( 1/2 ) m _{1} v _{1}^{2}}{( 1/2 ) m _{2} v _{2}^{2}} = \frac{m _{1}^{2} v _{1}^{2}}{m _{2}^{2} v _{2}^{2}} \cdot \frac{m _{2}}{m _{1}} = \frac{m _{2}}{m _{1}}$

Q. A stationary particle explodes into two particles of masses m1​ and m2​ which move in opposite directions with velocities v1​ and v2​. The ratio of their kinetic energies E1​/E2​ is

1

m1​v2​/m2​v1​

m2​/m1​

m1​/m2​

m1​v1​=m2​v2​ (conservation of linear momentum) E2​E1​​=(1/2)m2​v22​(1/2)m1​v12​​=m22​v22​m12​v12​​⋅m1​m2​​=m1​m2​​

Q. A stationary particle explodes into two particles of masses $m_{1}$ and $m_{2}$ which move in opposite directions with velocities $v_{1}$ and $v_{2}$ . The ratio of their kinetic energies $E_{1} / E_{2}$ is

$1$

$m_{1} v_{2} / m_{2} v_{1}$

$m_{2} / m_{1}$

$m_{1} / m_{2}$

$m_{1} v_{1} = m_{2} v_{2}$ (conservation of linear momentum)
$\frac{E _{1}}{E _{2}} = \frac{( 1/2 ) m _{1} v _{1}^{2}}{( 1/2 ) m _{2} v _{2}^{2}} = \frac{m _{1}^{2} v _{1}^{2}}{m _{2}^{2} v _{2}^{2}} \cdot \frac{m _{2}}{m _{1}} = \frac{m _{2}}{m _{1}}$