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Laws Of Motion

Question
CBSEENPH11020607

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m/s and the second part of mass 2 kg moves with second part of mass 2 kg moves with 8 m/s speed. If the third part flies off with 4 m/s speed, then its mass is,

  • 3 kg

  • 5 kg

  • 7 kg

  • 17 kg

Solution

B.

5 kg

We have,
p1 + p2 + p3 = 0 [ because p = mv]
Therefore,
1 x 12 i  + 2 x 8 j + p3 = 0
rightwards double arrow space 12 space straight i space plus space 16 space straight j space plus space straight p subscript 3 space equals space 0

rightwards double arrow space straight p subscript 3 space equals space minus left parenthesis 12 space straight i space space plus space 16 space straight j right parenthesis

therefore space straight p subscript 3 space equals space square root of left parenthesis 12 right parenthesis squared plus left parenthesis 16 right parenthesis squared end root

space space space space space space space space space space equals space square root of 144 space plus space 256 space end root

space space space space space space space space space space equals space 20 space kg minus straight m divided by straight s
Now. p3 = m3 v3
This implies,


straight m subscript 3 space equals space straight p subscript 3 over straight v subscript 3 space
space space space space space equals space 20 over 4 space
space space space space space equals space 5 space kg