Question

Two bodies have masses in the ratio 5 : 1 and kinetic energies in the ration 125 : 9. Calculate the ratio of their velocities.

April 18, 2024

Answer

Let mass of body A be m_A and body B be m_B. Let velocity of body A be v_A and body B be v_B.

Ratio of masses: $m_A\over m_B$ = $5\over 1$

Ratio of K.E: $KE_A\over KE_B$ = $125\over 9$

Now, $KE_A\over KE_B$ = ${{1\over 2}×m_A×v^2_A}\over {{1\over 2}×m_B×v^2_B}$

⇒ $125\over 9$ = ${m_A×v^2_A}\over {m_B×v^2_B}$

⇒ $125\over 9$ = $m_A\over m_B$ × ( $v_A\over v_B$ )²

⇒ $125\over 9$ = $5\over 1$ × ( $v_A\over v_B$ )²

⇒ ( $v_A\over v_B$ )² = $125\over 9$ × $1\over 5$

⇒ ( $v_A\over v_B$ )² = $25\over 9$

⇒ $v_A\over v_B$ = $\sqrt{25\over 9}$

⇒ $v_A\over v_B$ = $5\over 3$

∴ Ratio of their velocities = 5:3

💡 Some Related Questions

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(a) What is the potential energy of the pendulum at position B ?
(b) What is the total mechanical energy at point C?
(c) What is the speed of the bob at position A when released from position B ? (Take g = 10 ms^-2)

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