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In the question number 25, if the mass p...

In the question number 25, if the mass placed at vertex A is doubled, then the force acting on the mass 2m placed at the centroid O is

A

zero

B

`(2Gm^(2))/(l^(2))`

C

`(5Gm^(2))/(l^(2))`

D

`(6Gm^(2))/(l^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) Force on mass 2m at O due to mass 2m at A is
`F'_(OA)=(G(2m)(2m))/((1//sqrt(3))^(2))=(12Gm^(2))/(l^(2))` along OA
`:.` The resultant forece on the mass 2m at O due to masses at A,B and C is
`F'_(R)=F'_(OA)-(F_(OB) sin30^(@)+F_(OC) sin30^(@))`
`(12Gm^(2))/(l^(2))-((6Gm^(2))/(l^(2))xx(1)/(2)+(6Gm^(2))/(l^(2))xx(1)/(2))=0`
`= (12Gm^(2))/(l^(2))-(6Gm^(2))/(l^(2))=(6Gm^(2))/(l^(2))` along OA
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