Derive Newton's first law from second law?

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According to Newton’s second law of motion, the rate of change of momentum of a body is directly proportional to the applied force and it takes place in the direction in which the force acts.

Consider a body of mass m moving with velocity v, then the linear momentum of the body is given by

p = mv

Now from, Newton’s second law,

F ∝ \(\frac{dp}{dt}\)

⇒ F = k \(\frac{dp}{dt}\)

Where, k is constant of proportionality.

As, p = mv

⇒ F = k \(\frac{d(mv)}{dt}\) = km \(\frac{dv}{dt}\)

But, \(\frac{dv}{dt}\) = a, acceleration of the body

The value of the constant of proportionality k is considered as 1 for simplicity.

By taking k = 1, we get

F = ma

According to Newton’s first law of motion, everybody continues in its state of rest or uniform motion in a particular direction until and unless an external force is applied to change that state.

Now, if net force, F = 0, then by Newton’s second law acceleration, a = 0.

This shows that, if there is no force acting on the body, its acceleration is zero i.e. the body will be in its state of rest or uniform motion. Hence, Newton’s first law is derived from the second law.

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1.
Determine the current in the \( 3 \, \Omega \) branch of a Wheatstone Bridge in the circuit shown in the figure.

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Differentiate between inductive reactance, capacitive reactance and impedance of an ac circuit.
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\( 7.5 \times 10^2 \, \text{m}^{-1} \)
\( 1.5 \times 10^3 \, \text{m}^{-1} \)

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A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is \( \sqrt{2} \), and \( \sqrt{3} \).

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Derive Newton's first law from second law?

CBSE CLASS XII Related Questions

1.
Determine the current in the \( 3 \, \Omega \) branch of a Wheatstone Bridge in the circuit shown in the figure.

2.
Differentiate between inductive reactance, capacitive reactance and impedance of an ac circuit.
An ideal inductor and an ideal capacitor are connected in series across an ac voltage. Plot a graph showing variation of net reactance of the circuit with frequency of the applied ac voltage.

4.
The magnetic field in a plane electromagnetic wave travelling in glass (\( n = 1.5 \)) is given by \[ B_y = (2 \times 10^{-7} \text{ T}) \sin(\alpha x + 1.5 \times 10^{11} t) \] where \( x \) is in metres and \( t \) is in seconds. The value of \( \alpha \) is:

5.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

6.
A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is \( \sqrt{2} \), and \( \sqrt{3} \).

Similar Physics Concepts

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Derive Newton's first law from second law?

CBSE CLASS XII Related Questions

1. Determine the current in the \( 3 \, \Omega \) branch of a Wheatstone Bridge in the circuit shown in the figure.

2. Differentiate between inductive reactance, capacitive reactance and impedance of an ac circuit. An ideal inductor and an ideal capacitor are connected in series across an ac voltage. Plot a graph showing variation of net reactance of the circuit with frequency of the applied ac voltage.

4.The magnetic field in a plane electromagnetic wave travelling in glass (\( n = 1.5 \)) is given by \[ B_y = (2 \times 10^{-7} \text{ T}) \sin(\alpha x + 1.5 \times 10^{11} t) \] where \( x \) is in metres and \( t \) is in seconds. The value of \( \alpha \) is:

5.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

6.A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is \( \sqrt{2} \), and \( \sqrt{3} \).

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Determine the current in the \( 3 \, \Omega \) branch of a Wheatstone Bridge in the circuit shown in the figure.

2.
Differentiate between inductive reactance, capacitive reactance and impedance of an ac circuit.
An ideal inductor and an ideal capacitor are connected in series across an ac voltage. Plot a graph showing variation of net reactance of the circuit with frequency of the applied ac voltage.

4.
The magnetic field in a plane electromagnetic wave travelling in glass (\( n = 1.5 \)) is given by \[ B_y = (2 \times 10^{-7} \text{ T}) \sin(\alpha x + 1.5 \times 10^{11} t) \] where \( x \) is in metres and \( t \) is in seconds. The value of \( \alpha \) is:

5.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

6.
A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is \( \sqrt{2} \), and \( \sqrt{3} \).