Question

A particle is simultaneously acted upon by two forces of magnitudes $4N$ and $3N$. The net force on the particle is

• A. $7N$
• B. $5N$
• C. $1N$
• D. Between $1N$ snd $7N$.

Answer 1

The correct option is D Between $1N$ snd $7N$.

Let the two forces acting on the particle be $\overrightarrow{P}$ and $\overrightarrow{Q}$ of magnitude $4\text{N}$ and $3\text{N}$ and let $\overrightarrow{R}$ be the resultant force due to both forces. Then
$|\overrightarrow{R}|=\sqrt{P^2+Q^2+2PQ\cos \theta }$
$\Rightarrow$ $R$ depends upon $P,Q,\theta$
here $P=4,Q=3$
$\Rightarrow R_{max}=P+Q=7$ as the maximum value of $\cos \theta =1$
$R_{min}=P-Q=1$ as minimum value of $\cos \theta =-1$