Question

two object whose mass are in the ratio 3:2 are moving with speed in the ratio of 4:3 calculate the ratio of kinetic energy​

Answer 1

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Answer 2

Let mass of bigger object be M and mass of smaller object be m

Therefore

M:m=3:2

M/m=3/2

M=3m/2

Let velocity of bigger object be V and velocity of smaller object be v

Therefore,

V:v=4:3

V/v=4/3

V=4v/3

Kinetic energy of bigger object

=1/2 MV^2

=1/2 (3m/2)(4v/3)^2

=1/2 3m/2* 16v/9

=

$\frac{1}{2} \times \frac{3m}{2} \times \frac{16v}{9} \\ \\ = \frac{3m}{4} \times \frac{16v}{9} \\ \\ = \frac{36mv}{36} \\ \\ = 1mv$

Kinetic energy of smaller object =1/2mv^2

Therefore, ratio of kinetic energy

$\frac{ \frac{1}{2} mv^{2}}{mv} \\ = \frac{ \frac{1}{2}v }{1} \\ = \frac{1}{2} v$

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