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ICSE Class 10 Physics 2019 Paper

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Question : 3 of 74
Marks: +1, -0
Two bodies AA and BB have masses in the ratio 5:15: 1 and their kinetic energies are in the ratio 125:9125: 9. Find the ratio of their velocities.
Solution:  
Given:   mAmB=  51\; \frac{m_A}{m_B} = \; \frac{5}{1} and   KAKB=  1251\; \frac{K_A}{K_B} = \; \frac{125}{1}
We know,     K=  12mV2\; \; K = \; \frac{1}{2} m V^2
  ⇒V  =  2Km\; \Rightarrow V \; = \sqrt{ \; \frac{2K}{m} }
  ∴    VAVB  =  KAKB×  mBmA\; \therefore \; \; \frac{V_A}{V_B} \; = \sqrt{ \; \frac{K_A}{K_B} \times \; \frac{m_B}{m_A} }
  ⇒  VAVB  =  1259×  15\; \Rightarrow \; \frac{V_A}{V_B} \; = \sqrt{ \; \frac{125}{9} \times \; \frac{1}{5} }
⇒    VAVB  =  259=  53\Rightarrow \; \; \frac{V_A}{V_B} \; = \sqrt{ \; \frac{25}{9} } = \; \frac{5}{3}
  ∴  VA:VB  =5:3\; \therefore \; V_A : V_B \; = 5 : 3
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