Class IX – Gravitation

Ans. Sir Issac Newton

Ans. Henry Cavendish

Ans. N m²/kg²

(a) Mass – kg

(b) Weight – Newton

(i) Maximum – On earth the value of g is maximum at poles

(ii) Minimum – at equator the value of g is minimum

Ans.(i) F = G(2M)(m)/r²

F becomes doubled

(ii) F = GMm/(2r)²

F becomes ¼

Ans. The mass of stone is very small as compared to the mass of the earth. Due to very large mass the same gravitational force produces very small acceleration on earth.

Ans. An object is said to be in a state of free fall when it falls freely towards the earth due to gravitational force between the objects.

Ans. Zero (as acceleration due to gravity became zero at centre of earth

W = mg = 5 x 0 = 0

Ans. Both will reach at same time. This is because (g) acceleration due to gravity acting on body don’t depend on it mass hence both will reach at same time.

Application of universal law of gravitation:

1. The force binds us to earth

2. Motion of planets around sun.

3. Tides due to moon.

4. Motion of artificial satellites around earth

Ans.

Ans. Given that, the weight of the soil on the earth is 60 N.

g_earth = 10 ms^-2

Mass on the earth m₁ = 60/10 = 6 kg

Weight of the soil on moon = 10 N

g_moon = g_earth/6 = 10/6 ms^-2

Mass on moon m₂ = (10 x 6)/10 = 6 kg

Hence there has been no loss of the soil on moon and decrease in weight was due to difference in the gravity.

Initial velocity of the ball (u) = 49 m/s

Final velocity of the ball (v) = 0 m/s

Acceleration for upward motion (a) = -9.8 m/s²

Maximum height reached by the ball = h

                        v² – u² = 2gh

                        0 – (49)² = 2 x (-9.8) x h

                        H = 2401/19.6 = 122.5 m

Time taken to reach the maximum height, t

v = u + gt

t = (-49)/(-9.8)

t = 5 s

Since, same time is taken to reach the ground from the maximum height

So total time taken to return to the ground

                        = (2 x 5) = 10 s

Ans. The acceleration produced in a freely falling body by the gravitational pull of the earth is called the acceleration due to gravitation.

We know that,

Force = Mass x Acceleration

F = m x a

a = F/m ……. (1)

where F is the force on the object of mass m dropped from a distance r from the centre of earth of mass M

So, force exerted by the earth on the object is F = GMm/r² ……. (2)

M = Mass of earth

m = mass of object

r = distance of object from centre of earth

Now, from equation 1 and 2

a = G (M x m)/(r² x m)

a = G M/r²

Keplers first law – All planets move around sun in elliptical orbits with the sun at one of foci

Keplers second law – The line joining planets and the sun covers equal area in equal interval of time.

Keplers third law – The cube of mean distance of planet from the sun is directly proportional to square of time it takes to move around the sun.

r³ is directly proportional to t²

Ans. i) g on moon = g on earth x 1/6 = 9.8 x 1/6 = 1.63 m/s²

ii) W = mg

110.84 = m x g

m = 110.84/1.63

= 68 kg

iii) W = mg

W = 68 x 9.8 = 666.4 N

h = 180 m

t = ?

g = 9.8 m/s²

u = 0

h = ut + 1/2gt²

180 = 0 x t + ½ x 10 x t²

180 = 5 x t²

t² = 180/5 = 36

t = 6 sec

Ans. In this universe everybody attracts every other body with force which is directly proportional to product of their masses.

F ∝ m₁ x m₂ …… (1)

And is inversely proportional to square of distance between the two bodies

F ∝ 1/r² …… (2)

By combining eq (1) and (2) we get

F ∝ (m₁ x m₂)/r²

F = G x (m₁ x m₂)/r²