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Q.

Five point masses ' $m$ ' each are kept at five vertices of a regular pentagon. Distance of centre of pentagon from any one of the vertices is ' $a$ '. Find gravitational potential and field strength at centre.

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a

$\frac{- 10 G m}{a}, 0$

b

None of the above

c

$\frac{- 5 G m}{a}, 0$

d

$\frac{- 15 G m}{a}, 0$

answer is A.

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Detailed Solution

$V = 5 (\frac{- G m}{a}) = - \frac{5 G m}{a}$

For E Five vectors of equal magnitudes, when added as per polygon law of vector addition make a closed regular pentagon. Hence, net $E$ is zero.

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Five point masses ' m ' each are kept at five vertices of a regular pentagon. Distance of centre of pentagon from any one of the vertices is ' a '. Find gravitational potential and field strength at centre.