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Motion In Straight Line

Question
CBSEENPH11020610
Wired Faculty App

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2 m, 4 m, 8 m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be

  • -G

  • negative 8 over 3 G
  • negative 4 over 3 G

  • -4G

Solution

D.

-4G

The resulting gravitational potential is,
space space space space space straight V space equals space minus 2 straight G space open square brackets 1 over 1 plus 1 half plus 1 fourth plus 1 over 8 plus... close square brackets rightwards double arrow space straight V space equals space minus 2 straight G space open square brackets 1 plus 1 half plus 1 over 2 squared plus 1 over 2 cubed plus... space close square brackets rightwards double arrow space straight V space equals space minus 2 straight G space open parentheses 1 plus 1 half close parentheses to the power of negative 1 end exponent rightwards double arrow space straight V space equals space minus fraction numerator 2 straight G over denominator open parentheses 1 minus begin display style bevelled 1 half end style close parentheses end fraction space space space space space space space space space equals space minus fraction numerator 2 straight G over denominator open parentheses begin display style bevelled 1 half end style close parentheses end fraction space space space space space space space space space equals space minus space 4 straight G

Some More Questions From Motion in Straight Line Chapter

What is rest?

What is motion?

Is absolute rest or absolute motion possible?

What is the most essential thing to study the motion of a body?

Can a body be always at rest in some frame?

Can a body be in motion in the frame associated with the body itself?

When an object in motion can be considered as particle or point object?

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

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