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  • Tell me? Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m,8 m,......., respectively,from the origin. The resultinggravitational potential due to this system at the origin will be:

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1 m, 2 m, 4 m, 8 m,......., respectively,

from the origin. The resulting gravitational potential due to this system at the origin will be:

  • Option 1)

    -4G

  • Option 2)

    -G

  • Option 3)

    -\frac{8}{3}\text{G}

  • Option 4)

    -\frac{4}{3}\text{G}

 

Answers (1)

As we discussed in

Gravitational potential due to a mass m at distance r from it is V\:=\:-\frac{4M}{r}

Resultant gravitational potential

= -\:[\frac{G.M}{1}+\frac{GM}{2}+\frac{GM}{4}+\:------\propto]

= - GM (r+\frac{1}{2}+\frac{1}{4}+---+\propto)

= \frac{-GM}{1-\frac{1}{2}}\:=\:-2GM

= -2x6.2x4

V= - 4G

 


Option 1)

-4G

This option is correct.

Option 2)

-G

This option is incorrect.

Option 3)

-\frac{8}{3}\text{G}

This option is incorrect.

Option 4)

-\frac{4}{3}\text{G}

This option is incorrect.

Posted by

Sabhrant Ambastha

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