Question

In which case of a moving body, force is not needed?
(A) to increase the speed of the body
(B) to decrease the momentum of the body
(C) to change the direction of motion
(D) to keep the body in uniform velocity

Answer 1

Hint: By using the statement of Newton's first law of motion, the solution of the given condition can be determined. And also, by using the relation of the terms which are given in the option to the force and then the solution can be easily determined.

Complete step by step answer:
1. To increase the speed of the body:
The relation between the velocity and force is given by,
$F = m \times a$
Where, $F$ is the force, $m$ is the mass and $a$ is the acceleration.
Now, the acceleration is written as the velocity by time, then
$F = m \times \dfrac{v}{t}$
Where, $v$ is the velocity and $t$ is the time.
By the above equation, to increase the speed or velocity the force is needed.

2. To decrease the momentum of the body:
The relation between the force and momentum is given by,
$F = \dfrac{{dp}}{{dt}}$
Where, $F$ is the force, $dp$ is the change in momentum and $dt$ is the change in time.
By the above equation, to decrease the momentum of the body the force is needed.

3. To change the direction of motion:
There is no formula relation for the force and direction, but theoretically one statement is there. For example, if the car or any other vehicle or moving object is travelling in a road, if the moving object is subject to change its direction or it takes a turn, then the speed of the car is reduced. Another example, if we drive the car and turn the car at that instant, we reduce the speed of the car. As we discussed earlier to change the speed of the body the force is needed, so to change the direction the force is also needed.

4. To keep the body in uniform velocity:
According to the law of inertia or Newton's first law of motion, if the body is in rest or in uniform motion will remain in the same state of rest or uniform motion unless the external force will act on it. So, by keeping the uniform velocity of the body, the force is not needed.

Hence, the option (D) is the correct answer.

Note: In general, the object is in rest at that time the force is needed to change the velocity of the object or body. Once the object or body reaches the uniform velocity, the force is not required. Again, to change the velocity, then only the force is required.