What is the Universal law of gravitation?

Force of attraction between two masses \(m_1\) and \(m_2\) is given by,

$$ F = \frac{m_1 m_2}{r^2}$$

Where,
r is the distance between two masses \(m_1\) and \(m_2\).
G is a constant, called the Universal gravitational constant.

That is called Universal law of gravitation.

What does elasticity mean?

The property of a body, by virtue of which it tends to regain its original size and shape when the applied force is removed is known as elasticity.

Hooke’s law

Within elastic limit, the strain is proportional to stress. That is Hooke’s law.

Stress ∝ Strain
Stress = k × Strain

Where k is constant, called the Modulus of the elasticity.

Elastic energy per unit volume is given by,
ε = ½ × Y × σ2
Where,
Y is young’s modulus of elasticity.
σ is the strain.

Modulus of elasticity

According to Hooke’s law

Stress ∝ Strain

or Stress = k × Strain

$$ k = \frac{Stress}{Strain}$$

Where k is a constant, called the modulus of elasticity or coefficient of elasticity.

Types of Modulus of elasticity

1. Young’s modulus of elasticity or Young’s modulus

Young’s modulus of elasticity or Young’s modulus is given by,

$$ Y = \frac{\sigma}{\epsilon}$$

Where $$ \sigma$$ is normal stress and $$ \epsilon$$ is longitudinal strain.

We know that

$$ \sigma = \frac{F}{A}$$ and $$ \epsilon =\frac{\Delta L}{L}$$

So $$ Y = \frac{F L}{A \Delta L}$$

2. Bulk modulus

Bulk modulus is given by,

$$ B = \frac{\sigma_v}{\epsilon_v}$$

Where $$ \sigma_v$$ is normal stress and $$ \epsilon_v$$ is volumetric strain.

We know that

$$ \sigma_v = \frac{F}{A}$$ and $$ \epsilon_v = \frac{\Delta V}{V}$$

So $$ B = \frac{F V}{A \Delta V}$$

Modulus of rigidity

Modulus of rigidity is given by

$$ G = \frac{\sigma_s}{\theta}$$

Where $$ \sigma_s$$ is tangetial stress and $$ \theta$$ is shearing strain.

Poisson’s ratio

Poisson’s ratio is given by,
$$ p.r. =-\frac{d/D}{l/L}$$
where, l/L is the longitudinal strain and d/D is the lateral strain.