Question

two bodies are equal mass are moving with uniform velocities v and 2v find the ratio of theid kinetic energy ​

Answer 1

Answer:

let,

mass of A = m

mass of B = m  ( given masses are equal )

velocity of body A = v

velocity of body B = 2v

ratio of the bodies = k.e.of A / k.e.of B

                          = 1/2*mv^2 / 1/2*m(2v)^2

                          = 1/4 = 1:4

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Answer 2

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Given :- }}}$

$\to\textsf{ Two bodies are of equal masses.}\\\textsf{ \to They are moving with velocities v and 2v.}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: To \ Find :- }}}$

$\textsf{ \to The ratio of their Kinetic energies .}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Answer :- }}}$

Here let's take the mass of the body be m . Now we know that the kinetic energy of an object is given by half the product of its mass and square of Velocity that is ½mv² . So , hence here,

$\sf:\implies \pink{ K.E._1 : K.E._2 = \dfrac{1}{2}m(Velocity_1)^2 : \dfrac{1}{2}m(Velocity_2)^2 }\\\\\sf:\implies K.E._1 : K.E._2 = (v)^2 : (2v)^2 \\\\\sf:\implies K.E._1 : K.E._2 = v^2:4v^2 \\\\\sf:\implies K.E._1 : K.E._2 = \dfrac{v^2}{4v^2} \\\\\sf:\implies K.E._1 : K.E._2 = \dfrac{1}{4} \\\\ \sf:\implies\boxed{\pink{\mathfrak{K.E._1 : K.E._2 = 1:4}}}$

$\underline{\underline{\blue{\sf \therefore Hence \ the \ required \ ratio \ is\ \textsf{\textbf{ 1:4}}.}}}$