If the linear momentum of a moving object gets doubled due to application of a force, then its kinetic energy will

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CDS GK Previous Paper 10 (Held On: 8 Nov 2020)
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  1. remain same
  2. to increase by four times
  3. to increase by two times
  4. to increase by eight times

Answer (Detailed Solution Below)

Option 2 : to increase by four times
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Detailed Solution

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The correct answer is to increase by four times.

  • The momentum of an object is equal to the product of the mass of the object and its velocity.

Key Points

  • Let us display this with p.
  • Its vector sign is in the direction of velocity.
  • Its SI unit is "kg-meter / second".
  • Suppose the mass of the body be represented by 'M' and velocity be represented by 'V'.
  • If 'p' denotes the momentum of the body.
  • p = MV
  • if momentum gets doubled, If no mass was added, the velocity must've doubled.
    • i.e. V = 2V
  • \(Kinetic\space Energy = \frac{mv^2}{2} = \frac{p^2}{2m} = 4\frac{p^2}{2m}\), where 'p' is the linear momentum of the body.
  • Since 'p' becomes doubled, hence the kinetic energy will increase by a factor of 4.

Important Points

  • If a body is moving in a horizontal circle then its kinetic energy is the same at all points, but if it is moving in a vertical circle, then the kinetic energy is different at different points. 
  • Either potential energy is a form of energy that results from an object's position or arrangement of parts. It is stored energy that can become kinetic energy.
  • The measurement of potential energy in an object is calculated based on its mass and its height or distance.
  • PE = mgh.


where;

m = mass of the body

g = acceleration due to gravity

h = height 

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