Two bodies of masses m1 and m2 have equal momentum. Their kinetic energies E1 and E2 are in the ratio

Question

Two bodies of masses m1 and m2 have equal momentum. Their kinetic energies E1 and E2 are in the ratio (A)  √m1:√m2  (B)  m1:m2  (C)  m2:m1  (D)  m12:m22

Tardigrade Admin · Accepted Answer

Kinetic energy E=(P2/2 m) if bodies possess equal linear momenta, then E propto (1/m) ie, (E1/E2)=(m2/m1)

Q. Two bodies of masses $m_{1}$ and $m_{2}$ have equal momentum. Their kinetic energies $E_{1}$ and $E_{2}$ are in the ratio

$m_{1} : m_{2}$

$m_{1} : m_{2}$

$m_{2} : m_{1}$

$m_{1}^{2} : m_{2}^{2}$

Kinetic energy $E = \frac{P ^{2}}{2 m}$
if bodies possess equal linear momenta,
then $E \propto \frac{1}{m}$
ie, $\frac{E _{1}}{E _{2}} = \frac{m _{2}}{m _{1}}$

Q. Two bodies of masses m1​ and m2​ have equal momentum. Their kinetic energies E1​ and E2​ are in the ratio

m1​:​m2​​

m1​:m2​

m2​:m1​

m12​:m22​

Kinetic energy E=2mP2​ if bodies possess equal linear momenta, then E∝m1​ ie, E2​E1​​=m1​m2​​

Q. Two bodies of masses $m_{1}$ and $m_{2}$ have equal momentum. Their kinetic energies $E_{1}$ and $E_{2}$ are in the ratio

$m_{1} : m_{2}$

$m_{1} : m_{2}$

$m_{2} : m_{1}$

$m_{1}^{2} : m_{2}^{2}$

Kinetic energy $E = \frac{P ^{2}}{2 m}$
if bodies possess equal linear momenta,
then $E \propto \frac{1}{m}$
ie, $\frac{E _{1}}{E _{2}} = \frac{m _{2}}{m _{1}}$