Two particles of equal mass m have respective initial velocities u^i and u(^i+^j2)They collide completely inelastically. The energy lost in the process is
A
18mu2
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B
34mu2
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C
√23mu2
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D
13mu2
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Solution
The correct option is A18mu2 Step 1: Find the common velocity of the particles.
The given collision is completely inelastic and both the particles will stick together and move with common velocity.
From conservation of linear momentum. mu^i+mu(^i+^j2)=(m+m)v v=34u^i+u4^j |v|=u4√10
Step 2: Find the final and kinetic energy of the system
Final kinetic energy =122m(u4√10)2=58mu2
Initial kinetic energy=12mu2+12m(u√2)2=68mu2
Step 3: Calculate the energy lost in the process.
Loss in K.E=ki−kf=18mu2