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

$$\begin{array}{rl}& M=\frac{g{R}^2}{G}\simeq {10}^{25}kg\\ & M\to \text{ mass of earth }\end{array}$$

$G\to$ Gravitational constant

• Density of Earth

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

$\rho \to$ density of earth

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

• Inertial mass

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

From  Newton’s second law of motion

$$\begin{array}{rl}& F=m_{i}a\\ & m_i=\frac{F}{a}\end{array}$$

Where
$m_i\to$ inertial mass
$F\to$ external force

$$a\to ac{c}^n$$
 

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

$$F=\frac{GM{m}_g}{R^2}$$

So we get

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

Where $m_g=$ Gravitational mass
$I\to$ 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-$\left[ML{T}^{-2}\right]$ 

4. It is a vector quantity

5. It changes its value according to the value of g

6.  At $\mathrm{\infty }$ and at the center of the earth g = 0, So W is equal to zero there.