Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is

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Q.
Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is [2024]

1 $1 : \sqrt{3} : 2$

2 $1 : \sqrt{3} : \sqrt{2}$

3 $\sqrt{3} : \sqrt{2} : 1$

4 $\sqrt{2} : \sqrt{3} : 1$

Ans.
(1)

   $K_{A} = K_{B} = K_{C}$

Momentum $P = \sqrt{2 m K}$

   $P \propto \sqrt{m}$

   $P_{A} : P_{B} : P_{C} = \sqrt{m_{A}} : \sqrt{m_{B}} : \sqrt{m_{C}}$

$= \sqrt{400} : \sqrt{1200} : \sqrt{1600}$

   $= 20 : 20 \sqrt{3} : 40$

   $= 1 : \sqrt{3} : 2$

Solution

Q.
Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is [2024]

1 $1 : \sqrt{3} : 2$

2 $1 : \sqrt{3} : \sqrt{2}$

3 $\sqrt{3} : \sqrt{2} : 1$

4 $\sqrt{2} : \sqrt{3} : 1$

Ans.
(1)

   $K_{A} = K_{B} = K_{C}$

Momentum $P = \sqrt{2 m K}$

   $P \propto \sqrt{m}$

   $P_{A} : P_{B} : P_{C} = \sqrt{m_{A}} : \sqrt{m_{B}} : \sqrt{m_{C}}$

$= \sqrt{400} : \sqrt{1200} : \sqrt{1600}$

   $= 20 : 20 \sqrt{3} : 40$

   $= 1 : \sqrt{3} : 2$

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Solution

Q. Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is [2024]

1 1:3:2

2 1:3:2

3 3:2:1

4 2:3:1

Ans. (1) KA=KB=KC Momentum P=2mK P∝m PA:PB:PC=mA:mB:mC =400:1200:1600 =20:203:40 =1:3:2

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Q.
Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is [2024]

1 $1 : \sqrt{3} : 2$

2 $1 : \sqrt{3} : \sqrt{2}$

3 $\sqrt{3} : \sqrt{2} : 1$

4 $\sqrt{2} : \sqrt{3} : 1$

Ans.
(1)

$K_{A} = K_{B} = K_{C}$

Momentum $P = \sqrt{2 m K}$

$P \propto \sqrt{m}$

$P_{A} : P_{B} : P_{C} = \sqrt{m_{A}} : \sqrt{m_{B}} : \sqrt{m_{C}}$

$= \sqrt{400} : \sqrt{1200} : \sqrt{1600}$

$= 20 : 20 \sqrt{3} : 40$

$= 1 : \sqrt{3} : 2$