Question

The greatest and least resultant of two forces acting at a point are 10 N and 6 N respectively. If each force is
increased by 3 N, find the resultant of new forces when acting at a point at an angle of 90° with each other.
A)root 146
B)root 246
C)root 46
D)root 406​

Answer 1

Let two forces be x and y newtons.

=>Maximum resultant=10 N can only be when both forces act in the same direction.

so, x+y=10

=>Minimum resultant=6 N can only be when both forces act in opposite directions.

so, x-y=6

x=y+6

y+6+y=10

2y+6=10

2y=4=> y=2, x=8

New forces are, 5N and 11 N.

θ=90 degrees (angle between the two forces).

So, the resultant of the two forces 5N and 11N will be, root(5^2 + 11^2)

root(25+121)

root(146

Hence A) root 146 is the correct answer.