Sum of magnitude of two forces is 25 N. The resultant of these forces is normal to the smaller force and has a magnitude of 10 N. Then the two forces are

Options

A. 14.5 N, 10.5 N
B. 16 N, 9 N
C. 13 N, 12 N
D. 20N, 5N

Answer

A

Explanation

`F_(1) + F_(2)=25`
`implies F_(1)+ F_(2)cos theta=0`
`F_(res) = sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1) F_(2) cos theta)`
`implies 100 = F_(1)^(2) + F_(2)^(2) + 2F_(1) F_(2) cos theta `
`implies F_(1)^(2) + (25-F_(1))^(2) + 2F_(1) F_(2) cos theta=100`
`F_(1)^(2) + 625 + F_(1)^(2) -50F_(1) + 2F_(1) F_(2) cos theta= -525 `
`50F_(1)=525`
`F_(1) = 10.5, F_(2) = 25 - 10.5 = 14.5`.