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A body of mass $5\; kg$ is acted upon by two perpendicular forces $8 \;N$ and $6\; N.$ Give the magnitude and direction of the acceleration of the body
Solution

$2 \,m / s ^{2},$ at an angle of $37^{\circ}$ with a force of $8 \,N$
Mass of the body, $m=5\, kg$
The given situation can be represented as follows
The resultant of two forces is given as
$R=\sqrt{(8)^{2}+(-6)^{2}}=\sqrt{64+36}=10 \,N$
$\theta$ is the angle made by $R$ with the force of $8 \,N$ $\therefore \theta=\tan ^{-1}\left(\frac{-6}{8}\right)=-36.87^{\circ}$
The negative sign indicates that $\theta$ is in the clockwise direction with respect to the force of magnitude $8 \,N.$
As per Newton's second law of motion, the acceleration ( $a$ ) of the body is given as:
$F=m a$
$\therefore a=\frac{F}{m}=\frac{10}{5}=2 \,m / s ^{2}$