First slide

Torque

Question

The torque of a force $F = 2 \hat{i} - 3 \hat{j} + 5 \hat{k}$ acting at a point whose position vector $r = 3 \hat{i} - 3 \hat{j} + 5 \hat{k}$ about the
origin is [Kerala CEE 2013]

Easy

A

$- 3 \hat{i} + 5 \hat{k}$
B

$- 5 \hat{j} + 3 \hat{k}$
C

$- 5 \hat{j} - 3 \hat{k}$
D

$3 \hat{i} - 5 \hat{j} + 3 \hat{k}$

Solution

We know that, torque, $τ = r \times F$
Given, $F = 2 \hat{i} - 3 \hat{j} + 5 \hat{k}$
$\Rightarrow r = 3 \hat{i} - 3 \hat{j} + 5 \hat{k}$
Now, $τ = |\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 3 & - 3 & 5 \\ 2 & - 3 & 5 \end{array}|$
$τ = (- 15 + 15) \hat{i} - (15 - 10) \hat{j} (- 9 + 6) \hat{k}$
$τ = 0 - 5 \hat{j} - 3 \hat{k}$
$\Rightarrow τ = - 5 \hat{j} - 3 \hat{k}$

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