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# Mass And Density Of Earth - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• 7 Questions around this concept.

## Solve by difficulty

What is the standard value of acceleration due to gravity near the Earth's surface?

A planet has double the mass of the Earth. Its average density is equal to that of the Earth. An object weighing W on Earth will weigh on that planet:

## Concepts Covered - 1

Mass and Density of Earth
• Mass of earth-

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

$M=\frac{gR^{2}}{G}$ $\simeq \; 10^{25}kg$

$M\rightarrow$ mass of earth

$G\rightarrow$ Gravitational constant

• Density of earth

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

Where $\rho \rightarrow$ density of earth

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

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

• Inertial mass

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

From  Newton’s second law of motion

$F=m_{i}a$

So $m_{i}=\frac{F}{a}$

Where

$m_{i}\rightarrow$ inertial mass

$F\rightarrow$ external force

$a\rightarrow\: acc^{n}$

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 F= gravitational pull on a body of mass

applying Newton’s law of gravitation

We have $F=\frac{GMm_g}{R^2}$

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

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-$[MLT^{-2}]$

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 g = 0, So W is equal to zero there.

## Study it with Videos

Mass and Density of Earth

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