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The kinetic energy passessed by a body o...

The kinetic energy passessed by a body of mass m moving with a velocity v is equal to `(1)/(2)mv^(2)`, provided

A

The body moves with velocities comparable to that of light

B

The body moves with velocities negligible compared to the speed of light

C

The body moves with velocities greater than that of light

D

None of the above statement is correcst

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Verified by Experts

The correct Answer is:
B
Due to theory of relativity.
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Relation between kinetic energy and momentum Let us consider a body of mass 'm' having a velocity 'v', then momentum of the body P = mass xx velocity P = m xx v rArr v = (P)/(m) " "...(1) From definition, kinetic energy (K.E) of the body K.E = (1)/(2) mv^(2)" "...(2) Now putting the value of (1) in (2) we have K.E = (1)/(2)m ((P)/(m))^(2) K.E. = (1)/(2)m (P^(2))/(m^(2)) = (1)/(2) (P^(2))/(m) = (P^(2))/(2m)" "...(3) Thus we can write P^(2) = 2m xx K.E rArr P = sqrt(2m xx K.E) Thus momentum = sqrt(2 xx "mass" xx "kinetic energy") The kinetic energy of a given body is doubled. Its momentum will

Relation between kinetic energy and momentum Let us consider a body of mass 'm' having a velocity 'v', then momentum of the body P = mass xx velocity P = m xx v rArr v = (P)/(m) " "...(1) From definition, kinetic energy (K.E) of the body K.E = (1)/(2) mv^(2)" "...(2) Now putting the value of (1) in (2) we have K.E = (1)/(2)m ((P)/(m))^(2) K.E. = (1)/(2)m (P^(2))/(m^(2)) = (1)/(2) (P^(2))/(m) = (P^(2))/(2m)" "...(3) Thus we can write P^(2) = 2m xx K.E rArr P = sqrt(2m xx K.E) Thus momentum = sqrt(2 xx "mass" xx "kinetic energy") Two bodies of mass 1 kg and 4 kg possess equal momentum. The ratio of their kinetic energies is

ERRORLESS -WORK , ENERGY , POWER AND COLLISION-Ordinary Thinking (Objective Questions) (Conservation of Energy and Momentum)
  1. A light and a heavy body have equal momenta. Which one has greater K.E

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  2. A body at rest may have

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  3. The kinetic energy passessed by a body of mass m moving with a velocit...

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  4. If the momentum of a body is increased n times, its kinetic energy inc...

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  5. When work is done on a body by an external force, its

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  6. The bob of a simple pendulum (mass m and length l ) dropped from a hor...

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  7. From a stationary tank of mass 125000 pound a small shell of mass 25 p...

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  8. A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg . Th...

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  9. A bullet loses 1//20th of its velocity is passing through a plank. Wh...

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  10. A body of mass 2 kg is thrown up vertically with kinetic energy of 490...

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  11. Two masses of 1 gm and 4 gm are moving with equal kinetic energies. T...

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  12. If the K.E. of a body is increased by 300%, its momentum will increase...

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  13. A light body and a heavy body have same kinetic energy. Which one has ...

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  14. If linear momentum if increased by 50% then kinetic energy will be inc...

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  15. A free body of mass 8 kg is travelling at 2 mater per second in a stra...

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  16. If the K.E. of a particle is doubled, then its momentum will

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  17. If the stone is thrown up vertically and return to ground, its potenti...

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  18. A body of mass 2 kg is projected vertically upward with a velocity of ...

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  19. The energy stored in wound watch spring is

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  20. Two bodies of different masses m(1) and m(2) have equal momenta. Their...

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