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SUPER TET 2019 Paper I

Option 3 : will be two times of the initial value

हिन्दी विषय परीक्षा -1

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10 Questions
10 Marks
10 Mins

__Concept:__

Momentum

- Momentum is defined as the product of the mass and velocity of the body.
- It is a vector quantity directed toward velocity.
- It is given as

p = mv -- (1)

m is mass, v is the velocity, p is momentum

Kinetic Energy

- The energy of a body in motion due to its state of motion is called kinetic energy.
- It is given as

\(K = \frac{1}{2}mv^2\) --- (2)

K is kinetic energy, m is mass, v is speed.

Relationship between Momentum and Kinetic Energy

If we combine equation (1) and (2) we will get the relationship between momentum and kinetic energy as

\(K = \frac{p^2}{2m}\) -- (3)

Calculation:

So, let the initial kinetic energy of the body be K, momentum be p, and let its mass be m

Then from Equation (3)

\(K = \frac{p^2}{2m}\)

Or

p^{2} = 2mK -- (4)

Now, It is given Kinetic energy becomes 4 times of its initial value. Then, we can say that new kinetic energy is K' (K' = 4K) and new momentum is p'.

\(K '= \frac{p'^2}{2m}\)

or

p'^{2} = 2mK'

⇒ p'^{2} = 2m (4K)

⇒ p'2 = 4 (2m K)

⇒ p'2 = 4 p (From Equation 4)

Taking Square root of both side

⇒ p' ^{2} = 2 p

So, p' the final momentum is twice of initial momentum p.

**Therefore, the correct option is will be two times of the initial value.**