Question

The following pairs of forces act on a particle at an angle theta which can have any value
(a) 2 N and 3 N (b) 3 N and 3 N
(C) 2 N and 6 N and (d) 3 N and 8 N
The resultant of which pair cannot have a magnitude of
4 N?​

Answer 1

The correct option is (d) = 3N and 8N

This can be explained as:-

The forces of 3N and 8N can have a minimum resultant of 5N (8N-5N) when acting opposite to each other and have a maximum resultant of 13N(8N+5N) when acting in the same direction.

So, the range of resultant is from [5N,13N]. Therefore it cannot have have 4N as resultant no matter what is the angle between them.

Cheers!