Physics, asked by keshav2209, 11 months ago

Two bodies having masses m and 3m resp. are moving such that ratio of their momentum are 1:9. Find the ratio of their kinetic energies ​

Answers

Answered by nain31
8

GIVEN,

Mass of two bodies are in m and 3m.

Ratio of their momentum is 1:9

Let the common ratio be x,

so,

Momentum of first body = 1x

Momentum of second body = 9x

We know,

Kinetic \:energy =\dfrac{1}{2} \times m \times v^{2}

where m is the mass of the body and v is its velocity.

Since,

Momentum p= mv

v= \dfrac{p}{m}

On subsituting value of v ,

Kinetic \:energy =\dfrac{1}{2} \times m \times(\dfrac{p}{m})^{2}

Kinetic \:energy =\dfrac{p^{2}}{2m}

For first body,

Kinetic \:energy \: k_1 =\dfrac{1^{2}}{2m}

For second body,

Kinetic \:energy \: k_2 =\dfrac{9^{2}}{2 \times 3m}

Kinetic \:energy \: k_2 =\dfrac{81}{6m}

On dividing kinetic energy of first body by second,

\dfrac{K_1}{K_2} =\dfrac{1}{2m} \div \dfrac{81}{6m}\\\\\dfrac{K_1}{K_2} =\dfrac{1}{2m} \times \dfrac{6m}{81}\\\\\dfrac{K_1}{K_2} =\dfrac{6}{162} \\\\\dfrac{K_1}{K_2} =\dfrac{1}{27}

So the ratio of their kinetic energies will be 1:27.


Shruthi123456: Great answer @nain31 didi❤
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