Question

Out of the following the resultant of which cannot be 4 newton
1) 2 and 2
2) 2 and 4
3) 2 and 6 4) 2 and 8

Answer 1

Answer:

4)2 N and 8 N

The resultant is given by = R =

$\sqrt{\bold{A^{2}+B^{2}+2AB}cos\: \theta}$(by law of cosines)

Where A and B are the component vectors of R

1)Here A=2 N and B= 2 N

R=4 N = $\sqrt{8+8cos\: \theta}$

$\Rightarrow cos\: \theta=1$

which is possible

2)Here A=2 N and B= 4 N

R=4 N = $\sqrt{20+16cos\: \theta}$

$\Rightarrow cos\: \theta=\: -0.25$

which is possible

3)Here A=2 N and B= 6 N

R=4 N = $\sqrt{40+24cos\: \theta}$

$\Rightarrow cos\: \theta=\: -1$

which is possible

4)Here A=2 N and B= 8 N

R=4 N = $\sqrt{68+32cos\: \theta}$

$\Rightarrow cos\: \theta=\: -1.625$

But we know that $\bold{-1\le cos\: \theta \le 1}$

Hence,it is impossible that $cos\: \theta=\: -1.625$

So, OPTION D) is the required answer