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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A circular coil of 100 turns and radius \( \left(\frac{10}{\sqrt{\pi}}\right) \, \text{cm}\) carrying current of \( 5.0 \, \text{A} \) is suspended vertically in a uniform horizontal magnetic field of \( 2.0 \, \text{T} \). The field makes an angle \( 30^\circ \) with the normal to the coil. Calculate:
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Derive Newton's first law from second law?

CBSE CLASS XII Related Questions

1.
Nuclides with the same number of neutrons are called:

4.
In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.

5.
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:

6.
Assertion : In Young’s double-slit experiment, the fringe width for dark and bright fringes is the same. Reason (R): Fringe width is given by \( \beta = \frac{\lambda D}{d} \), where symbols have their usual meanings.

Similar Physics Concepts

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Derive Newton's first law from second law?

CBSE CLASS XII Related Questions

1.Nuclides with the same number of neutrons are called:

4.In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.

5.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:

6.Assertion : In Young’s double-slit experiment, the fringe width for dark and bright fringes is the same. Reason (R): Fringe width is given by \( \beta = \frac{\lambda D}{d} \), where symbols have their usual meanings.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Nuclides with the same number of neutrons are called:

4.
In a Young's double-slit experiment, two waves each of intensity I superpose each other and produce an interference pattern. Prove that the resultant intensities at maxima and minima are 4I and zero respectively.

5.
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:

6.
Assertion : In Young’s double-slit experiment, the fringe width for dark and bright fringes is the same. Reason (R): Fringe width is given by \( \beta = \frac{\lambda D}{d} \), where symbols have their usual meanings.