Mass And Density Of Earth MCQ - Practice Questions with Answers

• Mass of earth-

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

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

$G \rightarrow$ Gravitational constant

• Density of Earth

$$
g=\frac{4}{3} \pi \rho G R
$$
Where,

$\rho \rightarrow$ density of earth

$\mathrm{So}_0 \rho=\frac{3 g}{4 \pi G R}$
$\rho=5478.4 \mathrm{~kg} / \mathrm{m}^3$
 

• Inertial mass

Also known as the mass of material of the body which measures its inertia.

From  Newton’s second law of motion

$$
\begin{aligned}
& F=m_i a \\
& m_i=\frac{F}{a}
\end{aligned}
$$

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 the size, shape, and state of the body.

• Gravitational Mass-

It is mass that determines the gravitational pull acting upon it.

Let 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 measures 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 center of the earth g = 0, So W is equal to zero there.