An object of mass 'm' moving along a straight line with a velocity 'u' collides with a heavier mass 'M' and gets embedded into it. If the compound system of mass (m + M) keeps moving in the same direction the which of the given options is true?
(a) The kinetic energies before and after collision are same
(b) The kinetic energy after collision is 1/2(M+ m)u²
(c) There will be a loss of kinetic energy equal to 1/2 m²u²/(M+m)
(d) There will be a loss of kinetic energy equal to 1/2 Mn/(M+m) u²
Light1729:
option C is correct
Answers
Answered by
12
Let final velocity is V
Now, From law of conservation of momentum
mu = (M+m)V
V = mu/M+m
Initial KE = 1/2mu²
Final KE = 1/2mV² = 1/2(M+m)(mu/M+m)²
= 1/2 m²u²/(M+m)
Thus, Loss in kinetic energy
= 1/2mu²-1/2 m²u²/(M+m)
= 1/2mu² [ 1-m/M+m]
= mu²M/2(M+m)
Now, From law of conservation of momentum
mu = (M+m)V
V = mu/M+m
Initial KE = 1/2mu²
Final KE = 1/2mV² = 1/2(M+m)(mu/M+m)²
= 1/2 m²u²/(M+m)
Thus, Loss in kinetic energy
= 1/2mu²-1/2 m²u²/(M+m)
= 1/2mu² [ 1-m/M+m]
= mu²M/2(M+m)
Very well written
Answered by
5
C is thr right answer...
Attachments:
right
thnx
some use computer data to answer but proud.........taking time...using pen....page ...and mind is not so easy
really problim has been cracked in a great way
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