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
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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)
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