JEE Main 2024 — Laws Of Motion Question with Solution

To find the acceleration acting on the body, we first need to determine the resultant force acting on the body by adding the two forces ${\vec{F}}_1$ and ${\vec{F}}_2$ vectorially. Then, we apply Newton's second law of motion, which states that the acceleration $\vec{a}$ of a body is directly proportional to the total force $\vec{F}$ acting on it and inversely proportional to the mass $m$ of the body :

$$\vec{F}=m\cdot \vec{a}$$

or

$$\vec{a}=\frac{\vec{F}}{m}$$

Let's start by adding the forces:

$${\vec{F}}_1+{\vec{F}}_2=(5\hat{i}+8\hat{j}+7\hat{k})+(3\hat{i}-4\hat{j}-3\hat{k})$$

Performing the addition component-wise:

$${\vec{F}}_{\text{total}}=(5+3)\hat{i}+(8-4)\hat{j}+(7-3)\hat{k}{\vec{F}}_{\text{total}}=8\hat{i}+4\hat{j}+4\hat{k}$$

Now, let's use the formula for acceleration with $m=4\mathrm{kg}$:

$$\vec{a}=\frac{{\vec{F}}_{\text{total}}}{m}=\frac{8\hat{i}+4\hat{j}+4\hat{k}}{4\mathrm{kg}}$$

Divide each component by the mass:

$$\vec{a}=2\hat{i}+1\hat{j}+1\hat{k}$$

So, the acceleration acting on the body is:

$$\vec{a}=2\hat{i}+\hat{j}+\hat{k}$$

Thus, the correct option is:

Option A :

$$2\hat{i}+\hat{j}+\hat{k}$$