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Matter In Our Surroundings

Question
CBSEENSC9006348

Two bodies of equal masses move with uniform velocities of v and 3v respectively. Find the ratio of their kinetic energies.

Solution

Let space the space mass space of space each space body space be space straight m. space
straight K. straight E. space of space the space first space body comma space straight K subscript 1 space equals space 1 half mv squared
straight K. straight E. space of space the space second space body comma space straight K subscript 2 space equals space 1 half straight m left parenthesis 3 straight v right parenthesis squared
Ratio space of space the space kinetic space energies space equals space straight K subscript 1 over straight K subscript 2 space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator begin display style 1 half mv squared end style over denominator begin display style 1 half straight m. space 9 straight v squared end style end fraction

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 over 9 space equals space 1 space colon 9