Question

Two forces of $1N$ and $PN$ act at a point so that the magnitude of resultant is $1N$ and it is perpendicular to $1N$. The value of $P$ in newtons and the angle between the $1N$ and $PN$ are:

• A. $\sqrt{2},{135}^0$
• B. $\sqrt{2},{120}^0$
• C. $1,{45}^0$
• D. $2,{150}^0$

Answer 1

The correct option is A $\sqrt{2},{135}^0$

Let the $1N$ force point in the x direction, thus its vector representation would be $1\hat{i}$.
The resultant is $1N$ and is perpendicular to the initial $1N$ force. The vector representation of the resultant is $1\hat{j}$ .
Now let the unit vector along the direction of P N be $\hat{x}$.
Thus we get:
$1\hat{i}+P\hat{x}=1\hat{j}$ or $P\hat{x}=1\hat{j}-1\hat{i}$
The magnitude of this vector $\hat{j}-\hat{i}$ is $\sqrt{2}$ and if we plot it on the coordinate system we see that it makes an angle of ${135}^o$ with the horizontal.