Question
Download Solution PDFIf the kinetic energy of a body becomes 256 times its initial value, then the new linear momentum will be:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept: The 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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