Three particles, two with mass m and one with mass M, might be arranged in any of Rank the configuration according of the gravitational force on M, least to greatest.

Options

A. 1, 2, 3, 4
B. 2, 1, 3, 4
C. 2, 1, 4, 3
D. 2, 3, 4, 1

Answer

B

Explanation

`F_"on M"=G(Mm)/d^2+(GM m)/((2d)^2) =(GM m)/d^2 [1+1/4]=5/4xx(GM m)/d^2`

`F_"on M"=G(GMm)/d^2 -(GM m)/d^2=0`

`F_"on M"=GMm[(1/d^2)^2 + (1/d^2)^2]^(1/2)=sqrt2(GMm)/d^2`

`F_"on M"=(GMm)/d^2 sqrt(2+2cos theta ) = sqrt(2(1+cos theta))(GMm)/d^2`
Least to greatest : 2, 1, 3, 4