Q 11-03-140JEE MainJEE Main 2021 (27 Aug, Shift 1)Medium
The resultant of these forces $\overrightarrow{OP}$, $\overrightarrow{OQ}$, $\overrightarrow{OR}$, $\overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately ______ N. [Take $\sqrt{3} = 1.7$, $\sqrt{2} = 1.4$. Given $\hat{i}$ and $\hat{j}$ unit vectors along $x$, $y$ axis]
Answer: (B) $9.25\hat{i} + 5\hat{j}$
Resolve each force (angles measured from the $+x$ axis):
- $OP = 20$ N at $60^\circ$: $(10,\ 17)$
- $OQ = 10$ N at $30^\circ$: $(8.5,\ 5)$
- $OT = 15$ N at $150^\circ$: $(-12.75,\ 7.5)$
- $OS = 15$ N at $225^\circ$: $(-10.5,\ -10.5)$
- $OR = 20$ N at $-45^\circ$: $(14,\ -14)$
Sum: $x = 10 + 8.5 - 12.75 - 10.5 + 14 = 9.25$, $y = 17 + 5 + 7.5 - 10.5 - 14 = 5$.
Resultant $\approx 9.25\hat{i} + 5\hat{j}$ N.
Solution by Sreeraj P, M.Sc Physics