Question

Two bodies A and B have their masses in the ratio 3;1 an kinetic energy in the ratio 1;3find the velocity ratio

Answer 1

$\huge\underline{\underline{\bf\bigstar ANSWER \bigstar}}$

Let the mass of A be 3x and mass of B be x .

➤  Kinetic energy = ½ mv²

Ratio of their kinetic energy = 1 : 3

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$\sf \Longrightarrow\dfrac{ \dfrac{1}{2}m_1v_1^2}{\dfrac{1}{2}m_2v_2^2} = \dfrac{1}{3}\\\\\Longrightarrow 3(\dfrac{1}{2}m_1v_1^2)= \dfrac{1}{2}m_2v_2^2\\\\\Longrightarrow 3\times \dfrac{1}{2}\times 3x \ \times v_1^2 =\dfrac{1}{2} \times x \ \times v_2^2 \\\\\Longrightarrow 9 \times v_1^2= v_2^2\\\\\Longrightarrow \dfrac{v_1^2}{v_2^2}=\dfrac{1}{9}\\\\\Longrightarrow \dfrac{v_1}{v_2}=\sqrt{\dfrac{1}{9}} \\\\\Longrightarrow \bf \dfrac{v_1}{v_2}= \dfrac{1}{3}$  

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Ratio of their velocities = 1 : 3

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