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Motion In Straight Line

Question
CBSEENPH11020566

The force F acting on a particle of mass m is indicated by the force-time graph as shown below. The climate change in momentum of the particle over the time interval from zero to 8 s is,

  • 24 Ns

  • 20 Ns

  • 12 Ns

  • 6 Ns

Solution

C.

12 Ns

The area under F-t graph gives change in momentum.
For 0 to 2 s,
increment straight p subscript 1 space equals space 1 half straight x 2 straight x 6 space equals space 6 space kg minus straight m divided by straight s
For 2 to 4 sec,
increment straight p subscript 2 space equals space 2 space straight x space left parenthesis negative 3 right parenthesis space equals space minus 6 space kg minus straight m divided by straight s
For 4 to 8 sec,
increment straight p subscript 3 space equals space left parenthesis 4 right parenthesis straight x 3 space equals space plus 12 space kg minus straight m divided by straight s
So, total change in momentum for 0 to 8 sec is,
increment straight p subscript net space equals space increment straight p subscript 1 plus increment straight p subscript 2 plus increment straight p subscript 3

space space space space space space space space space space space equals left parenthesis plus 6 space minus 6 space plus 12 right parenthesis

space space space space space space space space space space space equals space 12 space kg minus straight m divided by straight s

space space space space space space space space space space space equals space 12 space Ns