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ICSE Class 10 Physics Question 1 of 20

Solved 2019 Question Paper ICSE Class 10 Physics — Question 2

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Question

Question 1(b)

Two bodies A and B have masses in the ratio 5:1 and their kinetic energies are in the ratio 125:9. Find the ratio of their velocities. [2]

Answer

Given,

mAmB=51KAKB=1259\dfrac{m_A}{m_B} = \dfrac{5}{1} \\[0.5em] \dfrac{K_A}{K_B} = \dfrac{125}{9}

Since,

KAKB=12mAvA212mBvB2=(mAmB)×(vA2vB2)\dfrac{K_A}{K_B} = \dfrac{\dfrac{1}{2}m_Av_A^2}{\dfrac{1}{2}m_Bv_B^2} \\[0.5em] = \Big(\dfrac{m_A}{m_B}\Big) \times \Big(\dfrac{v_A^2}{v_B^2}\Big)

Substituting the values we get,

1259=51×vA2vB2⇒vA2vB2=125×19×5⇒vAvB=259=53\dfrac{125}{9} = \dfrac{5}{1} \times \dfrac{v_A^2}{v_B^2} \\[0.5em] \Rightarrow \dfrac{v_A^2}{v_B^2} = \dfrac{125 \times 1}{9 \times 5} \\[0.5em] \Rightarrow \dfrac{v_A}{v_B} = \sqrt{\dfrac{25}{9}} = \dfrac{5}{3} \\[0.5em]

Hence, ratio between velocities of A and B is 5 : 3