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Two point masses A and B having masses i...

Two point masses A and B having masses in the ratio `4:3` are separated by a distance of 1m. When another point mass C of mass M is placed in between A and B, the force between A and C is `(1/3)^(rd)` of the force between B and C. Then the distance C from A is

A

`2/3m`

B

`1/3m`

C

`1/4 m`

D

`2/7 m`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the point mass C be placed at a distance of x m from the point mass A as shown in the figure.

Here `M_A/M_B =4/3`
The force between A and C is `F_(AC) =(GMM_A)/(x^2)` ...(i)
The force between B and C is `F_(BC) = (GMM_B)/((1- x)^2)` ....(ii)
According to given problem `F_(AC) = 1/3 F_(BC) `
`therefore (GM_AM)/(x^2) =1/3 ((GM_BM)/((1 -x)^2) ) ` (Using (i) and (ii)
or `(M_A)/(x^2) = (M_B)/(3(1 -x)^2) " or " M_A/M_B = (x^2)/(3(1 - x)^2)`
or `4/2 = (x^2)/(3 (1 - x)^2) rArr +2 = (x)/( 1 -x) " or " -2 = (x)/(1 -x)`
` rArr x = 2/3 m " or " 2m` ,only x = 2/3 m is possible for the given case.
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