Question 87: Laws of Motion

Question

A body of mass $4 \mathrm{~kg}$ experiences two forces $\vec{F}_1=5 \hat{i}+8 \hat{j}+7 \hat{k}$ and $\overrightarrow{\mathrm{F}}_2=3 \hat{i}-4 \hat{j}-3 \hat{k}$. The acceleration acting on the body is :

Accepted Answer

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:
$$
\vec{F}_{	ext{total}} = (5 + 3)\hat{i} + (8 - 4)\hat{j} + (7 - 3)\hat{k} \
\vec{F}_{	ext{total}} = 8 \hat{i} + 4 \hat{j} + 4 \hat{k}
$$
Now, let's use the formula for acceleration with $m = 4 \mathrm{~kg}$:
$$
\vec{a} = \frac{\vec{F}_{	ext{total}}}{m} = \frac{8 \hat{i} + 4 \hat{j} + 4 \hat{k}}{4 \mathrm{~kg}} 
$$
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 :
$$2 \hat{i}+\hat{j}+\hat{k}$$

Answer

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

Answer

$4 \hat{i}+2 \hat{j}+2 \hat{k}$

Answer

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

Answer

$2 \hat{i}+3 \hat{j}+3 \hat{k}$

Laws of Motion

A body of mass 4 \mathrm{~kg} experiences two forces \vec{F}_1=5 \hat{i}+8 \hat{j}+7 \hat{k} and \overrightarrow{\mathrm{F}}_2=3 \hat{i}-4 \hat{j}-3 \hat{k}. The acceleration acting on the body is :

Choose the correct answer: