Question

Please give clear answer.

Two objects having equal masses are moving with uniform velocity of 2m/s and 6m/s respectively. Calculate the ratio of their kinetic energies.

Answer 1

Please refer to the above attachment for expanation.....

Answer 2

$\huge \red { \boxed{ \boxed{ \mathsf{ \mid \ulcorner Answer : \urcorner \mid }}}}$

The masses of both bodies are same, So take mass as "m" .

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For 1st object :-

$\Large{\boxed{\sf{K.E \: = \: {\frac{1}{2}}mv^2}}}$

$\Large{\sf{K.E \: = \: {\frac{1}{2}}m(2)^2}}$

$\Large{\implies}{\boxed{\sf{K.E \: = \: {\frac{1}{2}}m4}}}----(1)$

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For 2nd object :-

$\Large{\boxed{\sf{K.E' \: = \: {\frac{1}{2}}mv^2}}}$

$\Large{\sf{K.E' \: = \: {\frac{1}{2}}m(6)^2}}$

$\Large{\implies}{\boxed{\sf{K.E' \: = \: {\frac{1}{2}}m36}}}----(2)$

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Divide (1) by (2)

$\LARGE{\sf{\frac{K.E}{K. E'}} \: = \: {\frac{{\cancel{{\frac{1}{2}}m}4}}{{\cancel{\frac{1}{2}m}36}}}}$

We get

$\LARGE{\sf{{\frac{K.E}{K. E'}} \: = \: {\frac{4}{36}}}}$

$\huge{\boxed{\boxed{\green{\sf{Ratio \: = \: 1:9}}}}}$