The sum of two forces at a point is 16N. if their resultant is normal to the smaller force and has a magnitude of 8N, then two forces are

Options

A. ` 6 newton and 10 newton `
B. ` 8 newton and `8` newton `
C. `4 newton and `12` newton `
D. `2` newton and `14` newton

Answer

A

Explanation

Here, ` A+ B= 16` …..(i)
` sqrt (a^2 + b^2 + 2 AB cos theta ) = 8 ` …(ii)
and ` tan 90^@ = ( B sin theta)/(A+ B cos theta)`
` or ` A= B cos theta = (B sin theta) /( tan 90^@) =0`
or ` B cos theta =- A` or cos theta =- B//A`
From ` (ii) , A^2 + B^2 + 1 AB (- B//A) = 64`
or ` A^2 - B^2 = 64` ....(iii)`
solving (i) and (iii) , we get `
` A= 10 N ` and ` B = 6 N`.