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Physics - Rotation Question with Solution | TestHub

PhysicsRotationTorque / angular accelerationMedium2 minPYQ_2021

PhysicsMediumnumerical

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

(Round off to the Nearest Integer)

Answer:

20.00

Solution:

$\vec{τ} = \vec{r} \times \vec{F}$

$\vec{r} = (2 \hat{i}) - (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) = - 3 \hat{j} - 4 \hat{k}$

and $\vec{F} = 4 \hat{i} + 3 \hat{j} + 4 \hat{k}$

$\vec{τ} = \vec{r} \times \vec{F} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & - 3 & - 4 \\ 4 & 3 & 4 \end{matrix}|$

$= \hat{i} (- 12 + 12) - \hat{j} (0 + 16) + \hat{k} (0 + 12)$

$= - 16 \hat{i} + 12 \hat{k}$

$∴ | \vec{τ} | = \sqrt{16^{2} + 12^{2}} = 20$

Stream:JEESubject:PhysicsTopic:RotationSubtopic:Torque / angular acceleration

⏱ 2mℹ️ Source: PYQ_2021

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