If the kinetic energy of a body becomes 256 times its initial value, then the new linear momentum will be:

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RRB ALP CBT I 14 Aug 2018 Shift 1 Official Paper
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  1. The same as the initial value
  2. 8 times the initial value
  3. 16 times the initial value
  4. 32 times the initial value

Answer (Detailed Solution Below)

Option 3 : 16 times the initial value
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ConceptThe relation between momentum and energy is given as:

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

Where, \(p \ \)is the momentum of particle.

\(m \ \)is the mass of the particle.

\(E \ \)is the kinetic energy of the particle.

Explanation:

The kinetic energy of the body becomes 256 times its initial value.

Let initial kinetic energy is E1=E with momentum \(p_1 \ \).

Final kinetic energy is E2=256E with momentum \(p_2 \ \).

Hence,

\(\frac{p_2}{p1} = \frac{(\sqrt{2mE_2})}{( \sqrt{2mE_1})}\\ p_2 = p_1 \times \frac{(\sqrt{2mE_2})}{( \sqrt{2mE_1})} = p_1 \sqrt{\frac{E_2}{E_1}} \\ So, p_2 =p_1\sqrt{ \frac{256E} { E}} = 16 p_1\)

Hence, final linear momentum is 16 times of its initial value.

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