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Question

A neutron of mass 1.67×1027kg is moving with a velocity 1.2×107ms1 collides head-on with a deuteron of mass 3.34×1027kg initially at rest. If the collision is perfectly inelastic, the speed of the composite particle will be

A
2×106ms1
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B
4×106ms1
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C
6×106ms1
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D
8×106ms1
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Solution

The correct option is B 4×106ms1
Mass of neutron (m) = 1.67×1027 kg. Speed of neutron (v) = 1.2×107ms1. Notice that the mass of deuteron (M) = 3.34×1027kg=2m. If V is the speed of the composite particle, the law of conservaton of momentum gives mv = (m+M)V
or V=mvm+M=mvm+2m
or V=v3=1.2×1073=4×106ms1, which is choice (b).

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