A body of mass 5 kg is moving with a velocity 10 metre per second. Find its kinetic energy .Find the ratio of initial kinetic energy and final kinetic energy if (A) its mass is doubled (B) its velocity is made three times.

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Solution

Dear Student ,
Here in this case the mass of the body , m = 5 kg and velocity = v = 10 m/s .
$S o, t h e k i n e t i c e n e r g y i s, E_{k} = \frac{1}{2} m v^{2} = \frac{1}{2} \times 5 \times 100 = 250 J (A) N o w w h e n t h e m a s s i s d o u b l e d t h e n, f i n a l k i n e t i c e n e r g y i s, E_{f} = \frac{1}{2} m' v^{2} = \frac{1}{2} \times 3 \times 5 \times 100 = 750 J S o, r a t i o o f i n i t i a l k i n e t i c e n e r g y t o f i n a l k i n e t i c e n e r g y i s, E_{i} : E_{f} = 250 : 750 = 1 : 3 (B) N o w w h e n t h e m a s s i s d o u b l e d t h e n, f i n a l k i n e t i c e n e r g y i s, E_{f} = \frac{1}{2} m v'^{2} = \frac{1}{2} \times 5 \times 900 = 2250 J S o, r a t i o o f i n i t i a l k i n e t i c e n e r g y t o f i n a l k i n e t i c e n e r g y i s, E_{i} : E_{f} = 250 : 2250 = 1 : 9$
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