Question

The formula for true force is

• A. $F=ma$
• B. $F=\frac{d\left(mv\right)}{dt}$
• C. $F=m\left(\frac{dv}{dt}\right)$
• D. $F=m\left(\frac{d^{2}x}{d{t}^2}\right)$

Answer 1

The correct option is B

$F=\frac{d\left(mv\right)}{dt}$

Explanation for the correct option:

In case of option B,

1. According to Newton's second law," A body's rate of change of momentum is proportional to the force applied to it, and this change in momentum occurs in the same direction as the applied force.
2. Force is directly proportional to rate of change of momentum.
3. That is, $F=\frac{d\left(mv\right)}{dt}$
4. A true force is characterized by rate of change of momentum where $v$ is velocity and $m$ is velocity dependent mass.
5. Thus, option b is the correct choice.

Explanation for the incorrect options:

In case of option A,

1. In $F=ma$ it is considered that mass is considered mass is independent of velocity.
2. In the above formula $m$ is mass independent of velocity and $a$ is acceleration.

In case of option C,

1. Also, in $F=m\left(\frac{dv}{dt}\right)$ mass is considered as constant.
2. In the above formula $\frac{dv}{dt}$ is rate of change of speed which is acceleration.

In case of option D,

1. In $F=m\left(\frac{d^{2}x}{d{t}^2}\right)$ also it is considered that mass is constant.
2. In the above formula $\frac{d^{2}x}{d{t}^2}$ is acceleration.

Hence, option B is the correct answer.