Question 416: Gravitation

Question

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 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

Accepted Answer

Gravitational potential  V = $${{ - Gm} \over r}$$
$${V_0} =  - {{G 	imes 2} \over 1} - {{G 	imes 2} \over 2} - {{G 	imes 2} \over 4} - {{G 	imes 2} \over 8}$$
= $$ - 2G\left[ {1 + {1 \over 2} + {1 \over 4} + {1 \over 8} + ...\infty } ight]$$
$$ =  - 2G 	imes {1 \over {1 - {1 \over 2}}}$$
$$ =  - 2G 	imes {1 \over {{1 \over 2}}} =  - 4G$$

Answer

$$ - {4 \over 3}$$ G

Answer

$$-$$ 4G

Answer

$$-$$ G

Answer

$$ - {8 \over 3}$$ G

Gravitation

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 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

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