Question

Two forces of magnitude 8N and 15N respectively act at a point. If the resultant force is 17N, the angle between the forces is:

• A. 60${}^0$
• B. 45${}^0$
• C. 90${}^0$
• D. 30${}^0$

Answer 1

Answer: (C)

90${}^0$

The resultant of two vectors:

$\overrightarrow{P}$ and $\overrightarrow{Q}$ is given by

$R=\sqrt{P^2+Q^2+2PQ\cos \theta }$

where, $P$ and $Q$ are magnitudes of two vectors and $\theta$ is the angle between two vectors.

Here $\theta =?$ $P=8NQ=15NR=17N$

Therefore,

$17=\sqrt{8^2+{15}^2+2\times 8\times 15\cos \theta }$

$289=64+225+240\cos \theta$

$289=289+240\cos \theta$

$289-289=240\cos \theta$

$cos\theta =0$

$cos\theta =\cos 90$

$\theta ={90}^0$