The sum of the magnitudes of two forces acting at a point is 16 N. The resultant of these forces is perpendicular to the smaller force which has a magnitude of 8 N. If the magnitude of smaller force is x, then the value of x is

Options

A. 2 N
B. 4 N
C. 6 N
D. 7 N

Answer

C

Explanation

` x + y = 16`,
Also, `y^(2)=8^(2)+x^(2)`
`" or "y^(2)=64+(16-y)^(2)[becausex=16-y]`
`"or "y^(2)=64+256+y^(2)-32y`
`"or "32y = 320`
y = 10 N
`therefore " "x + 10 =16 implies x = 6 N`