Question

Due to the application of a force on a body of mass $100\,kg$ that is initially at rest, the body moves with an acceleration of $20\,m{s^{ - 2}}$ in the direction of force. Find the magnitude of force.
A. $1000N$
B. $2000N$
C. $3000N$
D. $4000N$

Answer 1

Force is defined as the push or pull of an object that enables an acceleration in the body. Mathematically, force is the product of mass and the acceleration. On the other hand, we can say that force is an index of change in momentum of an object. Here, we will use the formula of force according to Newton’s second law of motion, that is, the product of mass and the acceleration.

Formula used:
The formula used for calculating the magnitude of force is given below
$F = ma$
Here, $F$ is the magnitude of force, $m$ is the mass of the body and $a$ is the acceleration in the body.

Complete step by step answer:
Here, consider a body of mass $100\,kg$and this body is initially at rest. When the body is moving, it will experience an acceleration of $20\,m{s^{ - 2}}$ in the direction of force.
Therefore, the mass of a body, $m = 100\,kg$
Also, the acceleration observed in the body, $a = 20\,m{s^{ - 2}}$
Now, the formula used for calculating the magnitude of force is given below
$F = ma$
Here, $F$ is the magnitude of force, $m$ is the mass of the body and $a$ is the acceleration in the body.
Now, putting the values in the above equation, we get
$F = 100 \times 20$
$\therefore \,F = 2000\,N$
Therefore, the magnitude of force applied on a body is $2000\,N$.

Hence, option B is the correct option.

Note: Here, the unit of force comes out to be $kg\,m{s^{ - 2}}$ which is also equal to $Newton$. A $Newton$ is the SI unit of force which is defined as the measure of force that is required to accelerate mass of one kilogram at a rate of one meter per second square. Here, we have not changed the units because both the terms have bigger units.