Gravitation Class 10 Chapter 1 Maharashtra Board Question and Answers

Q1.Study the entries in the following table and rewrite them, putting the connected items in a single row.

Concept	Unit / Description	Special Property
Mass	kg	Measure of inertia
Weight	N	Depends on height
Acceleration due to gravity	m/s²	Zero at the centre
Gravitational constant	Nm²/kg²	Same in the entire universe

2. Answer the following questions

a. Difference between mass and weight. Will they be the same on Earth and Mars?

Mass = amount of matter in an object. It is constant everywhere. Unit: kg.
Weight = force with which Earth (or any planet) pulls the object.
Formula: (g = gravity of that planet). Weight changes with planet.
On Mars:
- Mass remains same (e.g., 5 kg on Earth = 5 kg on Mars).
- Weight changes because Mars has smaller .

b. Definitions

(i) Free fall – When an object falls only under the influence of gravity (no air resistance, no other force).

(ii) Acceleration due to gravity () – The acceleration experienced by a freely falling object due to Earth’s pull. On Earth, .

(iii) Escape velocity – The minimum velocity required to escape a planet’s gravitational pull without further propulsion.
For Earth: .

(iv) Centripetal force – The force that keeps an object moving in a circular path. It acts towards the center.

c. Kepler’s three laws and how they helped Newton

Kepler’s laws (for planets around the Sun):

Law of orbits – Planets move in elliptical orbits with the Sun at one focus.
Law of areas – A line joining a planet to the Sun sweeps equal areas in equal times (planet moves faster when closer).
Law of periods – (square of time period ∝ cube of average distance from Sun).

How they helped Newton:
Newton used Kepler’s 3rd law () and the centripetal force formula
with to derive that the force of gravity follows the inverse square law:

d. Stone thrown upward: time up = time down

Let initial velocity = , height = .

Going up: final velocity , acceleration , time .
Using ⇒ ⇒ .
Coming down: initial velocity , acceleration , height .
Using and also (from upward motion). Solving gives .

Thus .

e. If becomes twice, why difficult to pull?

Friction while pulling = , and weight = .
If doubles, weight doubles, so normal force doubles, so friction doubles. Hence, twice as difficult.

3. Why is at Earth’s center?

Gravity at a distance The radius from the center (inside Earth) depends only on mass inside radius .
At the center , enclosed mass = 0. So gravitational force = 0. Hence .

4. Period of planet: if distance becomes

From Kepler’s 3rd law: .
So:

Thus . Proved.

5. Solve the following examples

a. a. An object takes 5 s to reach the ground from a height of 5 m on a planet. What is the value of g on the planet?

Formula:

Answer:

b. The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be the mass of B so that the value of g on B is half that of its value on A?

Given:
Formula:

So:

Cancel :

Multiply by 4:

Answer:

Planet B has twice the radius of planet A.
But we want gravity on B to be half of gravity on A.
To make that happen, planet B must have twice the mass of planet A.

c. The mass and weight of an object on earth are 5 kg and 49 N respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is 1/6th of that on the earth.

Ans: 5 kg and 8.17 N

Mass on Moon = same as Earth = (mass never changes).

Weight on Earth = ⇒ (consistent).

Weight on Moon =
= ≈

Answer: and

d. d. An object thrown vertically upwards reaches a height of 500 m. What was its initial velocity? How long will the object take to come back to the earth? Assume g = 10 m/s2 Ans: 100 m/s and 20 s

At top, , , .
Use ⇒
⇒ ⇒

Time to come back?
Time up: ⇒ ⇒
Total time =

Answer: and

e. A ball falls off a table and reaches the ground in 1 s. Assuming g = 10 m/s2 , calculate its speed on reaching the ground and the height of the table. Ans. 10 m/s and 5 m

Height of table:

Answer: and

f. f. The masses of the earth and moon are 6 x 1024 kg and 7.4×1022 kg, respectively. The distance between them is 3.84 x 105 km. Calculate the gravitational force of attraction between the two? Use G = 6.7 x 10-11 N m2 kg-2

Given:

Formula:

Multiply by :

= ≈

Divide by ≈

≈

Answer: (approx.)

g. The mass of the earth is 6 x 1024 kg. The distance between the earth and the Sun is 1.5x 1011 m. If the gravitational force between the two is 3.5 x 1022 N, what is the mass of the Sun? Use G = 6.7 x 10-11 N m2 kg-2 Ans: 1.96 x 1030 kg