Mass And Density Of Earth - Practice Questions & MCQ

• Mass of earth-

Using Newton’s law of gravitation we can estimate the mass of the earth

$
\begin{aligned}
& M=\frac{g R^2}{G} \simeq 10^{25} \mathrm{~kg} \\
& M \rightarrow \text { mass of earth } \\
& G \rightarrow \text { Gravitational constant }
\end{aligned}
$

- Density of earth

As $g=\frac{4}{3} \pi \rho G R$
Where $\rho \rightarrow$ density of earth
So $^\rho=\frac{3 g}{4 \pi G R}$

$
\rho=5478.4 \mathrm{~kg} / \mathrm{m}^3
$

- Inertial mass

Also known as the mass of material of body which measures its inertia.
From Newton's second law of motion

$
F=m_i a
$
 

${ }_{\text {So }} m_i=\frac{F}{a}$
Where
$m_i \rightarrow$ inertial mass
$F \rightarrow$ external force
$a \rightarrow a c c^n$
1. Gravity has no effect on inertial mass.
2. Inertial mass is independent of size, shape, and state of the body.
- Gravitational Mass-

It is mass which determines the gravitational pull acting upon it.
Let $\mathrm{F}=$ gravitational pull on a body of mass
applying Newton's law of gravitation

We have

$
F=\frac{G M m_g}{R^2}
$

So we get

$
m_g=\frac{F}{G M / R^2}=\frac{F}{I}
$
 

Where $m_g=$ Gravitational mass
$I \rightarrow$ Gravitational field intensity
Tip-Spring balance measure gravitational mass.
- Mass (m)
1. It is the quantity of matter contained in the body.
2. Its SI unit- Kg
3. Its dimension is $[M]$
4. It is a scalar quantity.
5. It Can never be zero
6. Its value does not change with g .
- Weight (W)
1. It is an Attractive force exerted by the earth on anybody.
2. S.I. Unit: Newton or Kg - wt
3. Dimension- $\left[M L T^{-2}\right]$
4. It is a vector quantity
5. It changes its value according to the value of $g$
6. At $\infty$ and at the centre of earth $\mathrm{g}=0$, So W is equal to zero there.