Correct Answer - Option 3 : two times its initial value
CONCEPT:
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Kinetic energy (K.E): The energy possessed by a body by the virtue of its motion is called kinetic energy.
The expression for kinetic energy is given by:
\(KE = \frac{1}{2}m{v^2}\)
Where m = mass of the body and v = velocity of the body
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Momentum (p): The product of mass and velocity is called momentum.
Momentum (p) = mass (m) × velocity (v)
The relationship between the kinetic energy and Linear momentum is given by:
As we know,
\(KE = \frac{1}{2}m{v^2}\)
Divide numerator and denominator by m, we get
\(KE = \frac{1}{2}\frac{{{m^2}{v^2}}}{m} = \frac{1}{2}\frac{{\;{{\left( {mv} \right)}^2}}}{m} = \frac{1}{2}\frac{{{p^2}}}{m}\;\) [p = mv]
\(\therefore KE = \frac{1}{2}\frac{{{p^2}}}{m}\;\)
\(p = \sqrt {2mKE} \)
CALCULATION:
Given that:
The kinetic energy of body becomes 4 times,
final momentum (p'):
\(p' = \sqrt {2mKE} = \sqrt {2m \times 4KE} = 2 \times \sqrt {2mKE} = 2p\)
