Question

If a rigid body is subjected to two forces $\overrightarrow{F_1}=2\hat{i}+3\hat{j}+4\hat{k}$ acting at $(3,3,4)$ and $\overrightarrow{F_2}=-2\hat{i}-3\hat{j}-4\hat{k}$ acting at $(1,0,0)$ then which of the following is (are) true?

• A. The body is in equilibrium
• B. The body is under the influence of a torque only
• C. The body is under the influence of a single force
• D. The body is under the influence of a force together with a torque

Answer 1

The correct option is A The body is in equilibrium

For a body to be in equilibrium, net force on it must be zero and should not generate any torque.

Here,

$\overrightarrow{F_1}=2\hat{i}+3\hat{j}+4\hat{k}$

$\overrightarrow{F_2}=-2\hat{i}-3\hat{j}-4\hat{k}$

Net force=$\overrightarrow{F_1}+\overrightarrow{F_2}$

$=0$

Taking torque about origin

$\tau =\overrightarrow{F_1}\times \overrightarrow{r_1}+\overrightarrow{F_2}\times \overrightarrow{r_2}$

$⟹(2\hat{i}+3\hat{j}+4\hat{k})\times (3\hat{i}+3\hat{j}+4\hat{k})+(-2\hat{i}-3\hat{j}-4\hat{k})\times \hat{i}$

$⟹(2\hat{i}+3\hat{j}+4\hat{k})\times (2\hat{i}+3\hat{j}+4\hat{k})$

$⟹\tau =o[\overrightarrow{A}\times \overrightarrow{A}=0]$

So, body will be in equilibrium.