Question

A body of mass 2kg moves vertically downwards with acceleration $a = 19.6m/{s^2}$. The force acting on the body simultaneously with the force of gravity is ($g = 9.8m/{s^2}$, neglecting air resistance).
(A) 19.6 N
(B) 19.2N
(C) 59.2N
(D) 58.8N

Answer 1

To find the force acting on the body, we need to find an expression for the forces that act on the body in all the directions. Then, we need to substitute the given values of the quantities in the expression and then we will get the answer.

Formula used: In this solution we will be using the following formula,
$\Rightarrow F = ma$
Where, $m$ is mass of the body, $a$ is the acceleration of the body, $F$ is the force due to acceleration of the body.
$\Rightarrow F = mg$
Where, $m$ is the mass of the body, $g$ is the acceleration due to gravity, $F$ is the force of gravity.

Complete step by step solution:
The forces acting the body would be the force due to the gravity acting downwards and the force caused due to the acceleration of the body.
The expressions for the two forces is given by,
$\Rightarrow F = ma$ Is the force caused by the acceleration of the body,
And $F = mg$ is the force of gravity.
Now, first we will calculate the force caused by the acceleration of the body. As given in the question, the mass of the body is $2kg$, the acceleration of the body is $a = 19.6m/{s^2}$. When we substitute these values in the expression, we get the result as,
$\Rightarrow F = 2 \times 19.6N$
So on calculating we get,
$\Rightarrow F = 39.2N$
Thus, the force on the body, due to its acceleration is $39.2N$.
Now, to calculate the force on the body due to gravity, we need to substitute the value of $m$ and $g$ on the expression. As we know that, the value of acceleration due to gravity equal to $g = 9.8m/{s^2}$, we get the answer as,
$\Rightarrow F = 2 \times 9.8N$
Therefore, on calculating we get
$\Rightarrow F = 19.6N$
Thus, the force of gravity is $19.6N$.
The total force on the body will be the difference between the force due to the acceleration and the force due to the gravity.
$\Rightarrow {F_{TOTAL}} = 39.2 - 19.6N$
On subtracting we get we have,
$\Rightarrow {F_{TOTAL}} = 19.6N$
Thus, the total forces acting on the body is $19.6N$.
Hence, the correct answer is option (A).

Note:
For the body, we can see two forces are acting on it. $F = mg$ is the force which is due to the gravitational pull of the earth. So the difference between these two forces will be the force that is acting on the body simultaneously with the force of the gravity.