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JEE Main 202116 MarchEvening Shift
Exam
JEE Main
Year
2021
Date
16 March
Shift
Evening Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2021 · 16 March · Evening Shift · Physics · Rotational Motion

A force → F = 4 ^ i + 3 ^ j + 4 ^ k is applied on an intersection...

A force \overset{\to}{F} = 4\overset{^}{i} + 3\overset{^}{j} + 4\overset{^}{k} is applied on an intersection point of x=2x = 2 plane and xx-axis. The magnitude of torque of this force about a point (2,3,4)\left(2, 3, 4\right) is ________.

(Round off to the Nearest Integer)

Correct answer

0

Step-by-step solution

τ→=r→×F→\overset{\to}{τ} = \overset{\to}{r} \times \overset{\to}{F}

\overset{\to}{r} = \left(2\overset{^}{i}\right) - \left(2\overset{^}{i} + 3\overset{^}{j} + 4\overset{^}{k}\right) = - 3\overset{^}{j} - 4\overset{^}{k}

and \overset{\to}{F} = 4\overset{^}{i} + 3\overset{^}{j} + 4\overset{^}{k}

\overset{\to}{τ} = \overset{\to}{r} \times \overset{\to}{F} = \left|\begin{cases}\overset{^}{i} & \overset{^}{j} & \overset{^}{k} \\ 0 & - 3 & - 4 \\ 4 & 3 & 4\end{cases}\right|

= \overset{^}{i}\left(- 12 + 12\right) - \overset{^}{j}\left(0 + 16\right) + \overset{^}{k}\left(0 + 12\right)

= - 16\overset{^}{i} + 12\overset{^}{k}

∴∣τ→∣=162+122=20∴ | \overset{\to}{τ} | = \sqrt{{16}^{2} + {12}^{2}} = 20

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