Question

Two masses m1 and m2 are in the ratio 1:4.They are moving with kinetic energy in the ratio 4:1 .What is the ratio of their moments

Answer 1

Answer:

ratio of momentum = $\sqrt{2*m1*k1}/\sqrt{2*m2*k2}$

Which is equal to $\sqrt{2*1*4}/\sqrt{2*4*1}$.

=$\sqrt{8}/\sqrt{8}$.

which is equal to 1:1.

Hope it helps.

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Explanation:

Answer 2

Given:

Ratio of two masses $m_{1}$ and $m_{2} =1:4$

Ratio of their Kinetic energy $=4:1$

To find:

Ratio of their momentum's.

Explanation:

• Kinetic energy of an object is said as the energy possessed by an object because of its velocity.

                        Mathematically, $KE=\frac{1}{2} mv^{2}$

• Momentum of a body is the velocity possessed by an object proportional to its mass.

                       Mathematically, $P=m$ × $v$

• That is an object having more mass will definitely have more momentum.

Multiplying mass (m) in numerator and denominator in equation of kinetic energy, we get

$K=\frac{1}{2}mv^{2}\frac{m}{m}$  

$K=\frac{1}{2}\frac{(mv)^{2} }{m}$

We know, $P=mv$

$K=\frac{P^{2} }{2m}$    $;$ or

$P^{2}=2mK$

$P=\sqrt{2mK}$

Solution:

For the first object  $m_{1}$,  let

Momentum $=P_{1}$    ;  Kinetic energy $=K_{1}$

For second object, let

Momentum $=P_{2}$    ;  Kinetic energy $=K_{2}$

Hence, the ratio of $P_{1}: P_{2}$ will be

$\frac{P_{1} }{P_{2} }= \frac{\sqrt{2m_{1} K_{1} } }{\sqrt{2m_{2} K_{2} } }$

$\frac{P_{1} }{P_{2} }= \sqrt{\frac{m_{1} }{m_{2} } \frac{K_{1} }{K_{2} }$

We have,

$\frac{m_{1} }{m_{2} }=\frac{1}{4}$    and   $\frac{K_{1} }{K_{2} }= \frac{4}{1}$

Hence, we get

$\frac{P_{1} }{P_{2} }=\sqrt{\frac{1}{4}* \frac{4}{1} }$

$\frac{P_{1} }{P_{2} } =\frac{1}{1}$

Final answer:

Hence, the ratio of momentum of the two bodies is $1:1$.

Although your question is incomplete, you might be referring to the question below.

Two masses m₁ and m₂ are in the ratio $1:4$ . They are moving with kinetic energy in the ratio $4:1$ . What is the ratio of their momentum's.