Newton's Laws Of Motion - Practice Questions & MCQ

1. Newton’s second law of motion:-

• It states that the acceleration of the particle measured from an inertial frame is given by the (vector) sum of all the forces acting on the particle divided by its mass (only when mass is constant), i.e.,

$
\vec{a}=\frac{\vec{F}}{m} \Rightarrow \vec{F}=m \vec{a}
$

- Impulse:
1. The quantity

$
\vec{I}=\int_{t_1}^{t_2} \vec{F} \cdot d t
$

time interval $\mathrm{t}_1$ to $\mathrm{t}_2$ and

Is equal to the change in the momentum of the body on which it acts, $P_f-P_1=\int_{P_1}^{P_1} d P=\int \frac{d P}{d t} * d t=\int F d t \Rightarrow$ Area under force and time graph is an impulse.

             2.    Dimension- MLT-1

            3.    Unit- kg-m/sec

• Impulse Momentum Theorem- Newton’s 2nd law can also be written as:

                      Rate of change in momentum = Force Applied

$
\vec{F}=\frac{d \vec{p}}{d t}
$

Inertial mass:
- This is defined by Newton's 2nd law- F = ma, which states that when a force F is applied to an object, it will accelerate proportionally, and that constant of proportion is the mass of that object.
- To determine the inertial mass, you apply a force of F Newtons to an object, measure the acceleration in $\mathrm{m} / \mathrm{s}^2$

$
\text { Inertial } \operatorname{mass}(k g)=\frac{F}{a}
$

2. Newton's third law of motion:-
- It states that "If a body A exerts a force F on another body B, then B exerts a force (-F) on A."
- Action and reaction never act on the same body.
3. Law of Conservation of Linear Momentum:
- As we know,

$
\vec{F}=\frac{d \vec{p}}{d t}, \text { If the net external force acting on the system is zero then the change in }
$

momentum of system $=0$

$
\begin{aligned}
& . \Rightarrow \Delta p=0 \\
& \therefore p_{\text {system }}=p_1+p_2+p_3+\ldots \ldots=\text { constant }
\end{aligned}
$