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 $\overrightarrow{F_2}=-2\hat{i}-3\hat{i}-4\hat{k}$ acting at (1, 0, 0) then which of the following is (are) true?

• A. The body maybe 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 maybe in equilibrium.

$\overrightarrow{F_1}+\overrightarrow{F_2}=0$

Now, $\overrightarrow{r_1}-\overrightarrow{r_2}=2\hat{i}+3\hat{j}+4\hat{k}$

Since, both forces $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$ are parallel to $\overrightarrow{r_1}-\overrightarrow{r_2}$, hence torque that is $\overrightarrow{r}\times \overrightarrow{F}=0$

Hence, there is no net force and no torque.

The body is under equilibrium.

Answer-(A)