The resultant of these forces → OP , → OQ , → OR , → OS and → OT is approximately ______ N . [Take 3 = 1 . 7, 2 = 1 . 4 Given ^ i and ^ j unit vectors along x, y axis]

Correct answer: B. 9 . 25 ^ i + 5 ^ j Resultant ( → R ) = ^ i (10 30 ° + 20 60 ° - 15 30 ° - 15 45 ° + 20 45 °) + ^ j (10 30 ° + 20 60 ° + 15 30 ° - 15 45 ° - 20 45 °) = 9 . 25 ^ i + 5 ^ j

JEE Main 202127 AugustMorning Shift

Exam: JEE Main
Year: 2021
Date: 27 August
Shift: Morning Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2021 · 27 August · Morning Shift · Physics · Mathematics in Physics

The resultant of these forces → OP , → OQ , → OR , → OS and → OT is...

The resultant of these forces $\overset{\to}{OP}, \overset{\to}{OQ}, \overset{\to}{OR}, \overset{\to}{OS}$ and $\overset{\to}{OT}$ is approximately ______ $N .$
[Take $\sqrt{3} = 1 . 7, \sqrt{2} = 1 . 4$ Given $\overset{^}{i}$ and $\overset{^}{j}$ unit vectors along $x, y$ axis]

The resultant of these forces → OP , → OQ , → OR , → OS and → OT is approximately ______ N . [Take 3 = 1 . 7, 2 = 1 . 4

Options

A $- 1 . 5\overset{^}{i} - 15 . 5\overset{^}{j}$
B $9 . 25\overset{^}{i} + 5\overset{^}{j}$
C $3\overset{^}{i} + 15\overset{^}{j}$
D $2 . 5\overset{^}{i} - 14 . 5\overset{^}{j}$

Correct answer

B. $9 . 25\overset{^}{i} + 5\overset{^}{j}$

Step-by-step solution

Resultant $( \overset{\to}{R} ) = \overset{^}{i}\left(10\cos 30 ° + 20\cos 60 ° - 15\cos 30 ° - 15\cos 45 ° + 20\cos 45 °\right)$

$+ \overset{^}{j}\left(10\sin 30 ° + 20\sin 60 ° + 15\sin 30 ° - 15\sin 45 ° - 20\cos 45 °\right)$

$= 9 . 25\overset{^}{i} + 5\overset{^}{j}$

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