Question

When a body is projected vertically up from the ground with certain velocity, its potential energy and kinetic energy at a point $$A$$ are in the ratio $$2 : 3$$. If the same body is projected with double the previous velocity, then at the same point $$A$$ the ratio of its potential energy to kinetic energy is

A
9:1
B
2:9
C
1:9
D
9:2
E
3:2

Solution

The correct option is C $$1 : 9$$Let in the first case, the total energy at the throwing point be $$5E$$.$$KE$$ at a particular height $$= 3E$$, potential energy at the height $$= 2E$$As velocity of thrown is doubled, kinetic energy becomes $$4$$ times.$$\therefore$$ Total $$KE$$ at the throwing point $$20\ E$$$$PE$$ at the same height $$= 2E$$ (will remain same as the previous value) and $$KE$$ at the same height $$= 18 E$$$$\dfrac {PE}{KE} = \dfrac {2E}{18E} = \dfrac {1}{9} = 1 : 9$$.Physics

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