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AIIMS 201925 May
Exam
AIIMS
Year
2019
Date
25 May
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

AIIMS 2019 · 25 May · Physics · Center of Mass, Momentum and Collision

Body A of mass 4 m moving with speed u collides with another body B...

Body AA of mass 4m4 m moving with speed uu collides with another body BB of mass 2m2 m at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body AA is

Options

  1. A5/95 / 9
  2. B1/91 / 9
  3. C8/98 / 9
  4. D4/94 / 9

Correct answer

C. 8/98 / 9

Step-by-step solution

Energy transferred to BB. Initial energy of B=B= zero Final velocity of vB=(m2−m1m1+m2)u2+2m1u1m1+m2m1=4m,u1=um2=2m,u2=0vB=2(4m)u6m=43u12m2vB212m1u12=122m(43)2u2124mu2\begin{aligned} & v_B=\left(\frac{m_2-m_1}{m_1+m_2}\right) u_2+\frac{2 m_1 u_1}{m_1+m_2} \\ & m_1=4 m, u_1=u \\ & m_2=2 m, u_2=0 \\ & v_B=\frac{2(4 m) u}{6 m}=\frac{4}{3} u \\ & \frac{\frac{1}{2} m_2 v_B^2}{\frac{1}{2} m_1 u_1^2}=\frac{\frac{1}{2} 2 m\left(\frac{4}{3}\right)^2 u^2}{\frac{1}{2} 4 m u^2} \\ & \end{aligned} Fraction of energy lost =8/9=8 / 9
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