NCERT Solutions for Class 9 Science Chapter 10 - Gravitation

Answer:

Newton’s universal law of gravitation states that every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
If m₁ and m₂ are the masses of two objects lying at a distance d apart, then force F between them is :

where, G is a constant called universal gravitational constant.

Answer:

Let m be the mass of an object on the earth’s surface and let mass of the earth be M. If R is the radius of the earth, the gravitational force between the earth and the object is

where, G is a constant called universal gravitational constant and its value is 6.67 x 10^-11 Nm²kg ^-2.

Answer:

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

Answer:

Acceleration due to gravity is the acceleration with which a body falls due to gravitational force of the Earth.

It is represented by g and its value is 9.8 ms^-2.

If a mass m is placed on the earth with mass M and radius R, then

But this force is also equal to the weight of the body i.e., F = mg

\

or

Answer:

Answer:

Let m be the mass of an object. Let its weight on the moon be W_m.

where M_m and _m are the mass and the radius of the moon respectively.
If mass and radius of the earth are M_e and R_e respectively, then the weight of the body We with mass m on the earth is:

From (i) and (ii), we have

Now M_m = 7.36 x 10²² kg ; M_e = 5.98 x 10²⁴ kg ;
R_e = 6.37 x 10⁶ m and R_m = 1.74 x 10⁶ m

\

Hence, weight of a body on the moon is 1/6th that on the earth.

Answer:

As the pressure exerted by an object is force per unit area.

Thus, a thin strap of small area will exert a large pressure on the student. Hence, it is difficult for the student to hold the bag with thin string.

Answer:

When a body is put in a liquid or gas, it experiences an upward force. Due to this upward force, substances appear lighter when immersed wholly or partially in a liquid. The tendency of a fluid (liquid or gas) to exert an upward force on the object is called buoyancy. The upward force that acts on the object is called buoyant force.

Answer:

When a body is immersed in water, two forces are acting on it:
(i) Weight, W, of the body acting vertically downwards.
(ii) Upward thrust, w, equals to the weight of water displaced.
Three cases arise:
(i) If W > w, i.e., the downward force due to weight of the body is greater than weight of the water displaced, the body will sink. Iron, stone etc., sink in water because W > w.
(ii) If W > w, the body will remain in equilibrium anywhere inside water. In this case, the net weight of the body in the water is zero. This happens when the density of the body is exactly equal to density of water displaced.
(iii) If W > w i.e., the weight of the body is less than the weight of water displaced, the body will be forced upwards. As it projects above the surface of water, volume of water (and hence weight of water) displaced will become less. The upward force will go on decreasing till it becomes equal to weight of the body. Now, the body starts floating.

Answer:

When we stand on a weighing machine, air exerts on upward force which makes us feel lighter than the real situation. Therefore, if in weighing machine, our mass is 42 kg, then our actual mass is more than 42 kg.

Answer:

Weighing machine measures weight and not the mass of the body. If the weight of cotton and iron is each equal to 100 kg, the real weight of cotton is more than that of iron. Due to larger volume of the cotton, the loss of weight when cotton is weighed in air is more than that of iron weighed in air. Therefore, the real weight (weight in vacuum) is more in case of cotton than that of iron.

Answer:

Force of attraction between two objects is inversely proportional to square of the distance between the objects, therefore, force of attraction will become four times when distance between them is reduced to half.

Answer:

Heavier bodies experience gravitational force in proportion to their masses but the acceleration with which they fall towards the earth is same for all bodies either heavier or lighter. Acceleration due to gravity g is same for all bodies.
We know that v = u + at = u + gt. As u = 0, v = gt. Since g is independent of the mass of the bodies, the velocity of all bodies will be equal after equal interval of time.

Answer:

G = 6.67 x 10^-11 Nkg^-2m²; m₁ = 1 kg ; m₂ = 6 x 10²⁴ kg ;
R = 6.4 x 10⁶ m ; F = ?

F =

F =

F = 0.977 x 10¹ = 9.77 N

Answer:

The earth and the moon attract each other with an equal force. The magnitude of force on each of the two bodies (moon and earth) is the same but the direction is opposite.

Answer:

Force of attraction due to gravitation provides the necessary centripetal force to the moon to enable it to move round the earth in almost a circular path. Acceleration is inversely proportional to mass of the Earth which is very large; therefore, acceleration produced in the earth is so small that it cannot be observed. Therefore, we cannot see the earth moving towards the moon.

Answer:

The force of attraction between two objects of mass m₁ and m₂ lying at a distance d apart is given by

(i) When mass of one of the objects (say m₁ or m₂) is doubled, F will be doubled.
(ii) When distance (d) between the two objects is doubled, F becomes one-fourth i.e., 1/4 times.
When distance (d) between the two objects is tripled (made 3 times), the force F between them is reduced to 1/9th of the original.
(iii) When both m₁ and m₂ are doubled, F becomes four times.

Answer:

The universal law of gravitation successfully explains that
(i) all bodies, small or large attract each other.
(ii) the gravitational force binds us to the earth.
(iii) the motion of the moon around the earth is due to gravitational force.
(iv) the motion of the earth and other planets around the sun is due to gravitational force.
(v) Artificial satellites move around the earth due to gravitational force.

Answer:

Acceleration of free fall is the acceleration with which a body falls towards the earth due to gravitational attraction of the earth. Its value is 9.8 ms^-2.

Answer:

It is called gravity.

Answer:

(Hint: The value of g is greater at the poles than at the equator)
The value of g is more at the poles than at the equator. Due to the elliptical shape of the earth, the radius of the earth is more at the equator than at the poles.

Now,

Thus, more R, lesser g ; lesser R, greater g.
Weight = mg hence, gold will weigh lesser at the equator. The friend at the equator will not agree as he is getting lesser weight of gold.

Answer:

A sheet of paper experiences larger force of friction due to air than a sheet that is crumpled into a ball. Area of contact between sheet and air is larger than the area of contact between air and crumpled sheet.
Increased force of friction will reduce the forward driving force more in case of sheet of paper than ball of crumpled sheet and hence, sheet will fall slower.

Answer:

Mass m = 10 kg, g_e (on the earth) = 9.8 ms^-2
Weight on the earth = mg_e = 10 x 9.8 = 98 N
Since gravitational force on the moon is 1/6th of that on the earth, g on the moon is also 1/6th of that on the earth

g_m (on the moon) =

Weight (on the moon) = mg_m = 10 x 1.633
W_m = 16.33 N

Answer:

u = 49 ms^-1; a = - 9.8 ms^-2 [going up];
v = 0 ms^-1 [at top],
s = h = ? ; t = ?
Using v² - u² = 2as, we have
(0)² - (49)² = 2 (- 9.8)h

h = 122.5 m
Using v = u + at, we have
0 = 49 - 9.8 t
or 9.8 t = 49

or

t = 5 s which is the time of ascent (going up).
Since, time of ascent = time of descent
\ Total time = 2t = 2 x 5 = 10 s

Answer:

u = 0; s = 19.6 m; a = 9.8 ms^-2; v = ?
Using v² - u² = 2as, we have
v² - (0)² = 2 (9.8) (19.6) = (19.6)²
v = 19.6 ms^-1

Answer:

u = 40 m
a = - 10 ms-2; s = h = ?
v = 0 ms-1 [at maximum height]
Using v2 - u2 = 2 as, we have
(0)² - (40)² = 2 (-10) h
h = 80 m
Maximum height attained = 80 m
Stone goes 80 m upwards and then returns to the point of throw by moving 80 m downwards.
\ Total distance covered = 80 + 80 = 160 m
Since it returns to the point of throw, therefore net displacement is zero.

Answer:

F = ?; m₁ = 6 × 10²⁴ kg; m₂ = 2 × 10³⁰ kg; d = 1.5 × 10¹¹ m

Answer:

Let the stones meet at a distance ‘x’ metres from the top.
Considering downward motion;
u = 0; s = x, a = 10 ms^-2

Using s =

x =

x = 5 t²... (i)
Considering upward motion (of second stone), we have
u = 25 ms^-1, a = - 10 ms^-2, s = (100 - x) m

Using s =

100 - x =

But from (i) 5 t² = x [from (i)]
\ 100 - x = 25t - x
or t = 4s
From (i), we have x = 5 (4)² = 80 m
\ The stones will meet at a distance 80 m from the top.

Answer:

(i) Since, time of ascent = time of descent
\ Time of ascent (going up to the top) =
Considering upward motion,
u = ?, a = - 9.8 ms^-2, v = 0 ms^-1 [at top]; t = 3 s , s = h = ?
Using v = u + at, we have
0 = u - 9.8 × 3 = u - 29.4
u = 29.4 ms^-1

(ii) Using s =

h =

h = 44.1 m
(iii) It took 3 s to reach the top. After 4 seconds from start, the ball was on downward journey for
4 - 3 = 1 s. Considering downward motion,
u = 0 ms^-1; t = 1s; a = 9.8 ms^-2; s = ?

s =

=

s = 4.9 m below the top

Answer:

The buoyant force acts on an object immersed in a liquid in the vertically upward direction.

Answer:

The weight of water displaced by a plastic block is more than its own weight. Upward force acting on the plastic block is therefore more than the downward force due to weight of the block. Due to excessive upward buoyant force, the block is forced upwards.

Answer:

Density of substance =

The density of substance (2.5 gcm^-3) is more than that of water (1 gcm^-3). Therefore, the substance will sink to the bottom.

Answer:

Density of packet =

Since the density of packet is more than that of water, therefore, the packet will sink to the bottom.
Mass of water displaced = Volume of water displaced × density of water

i.e.,

or m = 350 g