Question

If the system is in equilibrium ($cos53$${}^0$ = $3/5$), then the value of ${}^{\prime }P{}^{\prime }$ is

• A. $16N$
• B. $4N$
• C. $\sqrt{208}N$
• D. $\sqrt{232}N$

Answer 1

Answer: (C)

$\sqrt{208}N$

As the system is in equilibrium, sum of all vector forces will be zero.

$\overrightarrow{P}$ will have magnitude same as resultant of $\overrightarrow{A}$ and $\overrightarrow{B}$ and direction opposite to it.
$\therefore \left|\overrightarrow{P}\right|=\sqrt{A^2+B^2+2\overrightarrow{A}.\overrightarrow{B}}=\sqrt{36+100+72}=\sqrt{208}$N