chapter10 -GRAVITATION

1. Describe the fundamental principle of gravitation

Explanation:

According to the universal law of gravitation, every particle in the cosmos attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation.


2. What is the formula to calculate the gravitational force between an object on the earth's surface and the earth's centre?

Explanation:

The following is the formula to determine the strength of the gravitational attraction between the earth and an object on its surface:

F = G * M*m /d-2

where F is the gravitational force's strength.

G stands for the constant of gravitation.

M = Earth's mass m = Objects' mass

d is the separation between the objects and the earth's centre.


3. How do you define "free fall"?

Explanation:

The gravity of the Earth pulls each thing towards its core, as explained. When anything is dropped from a particular height, it starts to descend to Earth's surface due to the effects of gravity. Free fall is the term for such an item movement.


4. What do you mean by gravitational acceleration?

Explanation:

The gravitational force per unit mass that pulls one object towards another, explained. Acceleration due to gravity modifies velocity. 9.81 m/s-2 is the value. "g" stands for it.


5. What are the differences between the mass of an object and its weight ?

Explanation:

   Mass :

(i) Mass is the matter contained with in a volume.

(ii) It is constant in the whole universe.

(iii) It is measured in "kg"

   Weight :

(i) Weight is the gravitational force .

(ii) It is variable the value changes as per the requirement / location.

(iii) It is measured in "Newton" 


6. Why is it challenging to hold a school bag with a thin and sturdy string strap?

Explanation:

The bags' weight (force) will be the same because their masses are the same.

Although this strap has a smaller surface area than a standard belt, greater pressure will be applied because, as we all know, pressure equals force times area.


7. How would you define buoyancy?

Explanation:

A force known as "buoyant" is experienced when an object is partially or completely submerged in a liquid.


8. What causes an object to float or sink when it is placed on water's surface?

Explanation:

When an object comes into contact with the surface of a fluid, it is subject to two different types of forces: the gravitational force, which pulls the object below, and the buoyancy force, which pushes the object upward.


9. You weigh yourself and discover that it is 42 kg. Are you more than 42 kg in weight or less?

Explanation:

The explanation is that the air that surrounds us constantly thrusts upward. This force causes the weighing machine's reading to decrease. Actual weight ought to be greater than other apparent weights.


10. You have a sack of cotton and an iron bar, both of which, when weighed on a scale, indicate that they both weigh 100 kg. In truth, one weighs more than the other. Describe which one is heavier and why.

Explanation:

Fupthrust plus reading equals real weight (100 kg)

Real cotton weight is greater than real iron weight due to the greater upthrust caused by air molecules on the cotton bundle's bigger surface.


11. How does a halving of the distance between two objects affect the gravitational force between them?

Explanation:

According to the gravitational constant: - F = G*m1*m2/r-2

where G is the gravitational constant and r is the separation between the two bodies.

m = the total body mass

F has a direct relationship with 1/r-2 r = 1/2r.

F' equals G*m1*m2/1/r-2 F' equals 4G*m1*m2/r-2 F' equals 4F

As a result, the force will multiply four times.


12. All objects are subject to gravitational pull in proportion to their masses. Then why does a heavy object not fall to the ground more quickly than a light one?

Explanation:

Heavy items do not fall more quickly than light objects because: I All objects fall in free fall with a constant acceleration of "g" (gravitational acceleration).

(ii) The value of "g" is constant and independent of the mass of the objects. As acceleration ("g") is constant for a body of any objects of any mass, it appears as though forces are directly proportional to mass.


13. How much gravitational pull does the earth exert on a 1 kilogramme item resting on its surface? (The earth's mass is 6 1024 tonnes, and its radius is 6.4 106 metres.)

Explanation:

Hence, the body's mass, m, equals 1 kg.

 

Earth's mass is M=6 1024 kg.

R=6.4106m is the Earth's radius.

The magnitude of the gravitational force (F) between the earth and the body is determined by the universal law of gravity, where G=6.671011Nm2/kg2 denotes the gravitational constant.

Hence, F=GMmR2=6.671011610241(6.4106) gives the gravitational force (F) between the earth and the body.

2 \s = 9.77 N = 9.8 N (estimated) (approx)


14. There is a gravitational pull between the earth and the moon. Is the force with which the earth attracts the moon larger, less powerful, or the same as that with which the earth attracts the moon? Why?

Explanation:

The earth and moon are drawn to one another by the same gravitational force because their formulas for calculating the force of attraction are identical.

It can be expressed mathematically as F = G*m1*m2/d-2.


15. Why does the earth not gravitate towards the moon if the moon draws it?

Explanation:

Because the moon has a very little mass in comparison to the planet, the earth does not move in the direction of the moon.

Moon mass minus Earth mass


16. What happens to the force between two objects, if

(i) The mass of one object is doubled?

(ii) Are the objects' distances doubled and tripled?

(iii) Are both objects' masses doubled?

Explanation:

(i) The universal law of gravity states that F = G*M1*M2/r-2 F1 = G(M1)*(2M2)/r-2 F1 = 2F, meaning that the force doubles 

The universal law of gravity states that F = G*M1*M2/r-2 F1 

= G(M1)*(2M2)/r-2 F1 = 2F, meaning that the force doubles 

(ii) Fa = G(M1)*(M2)/2r-2 = F/4 Fb = G(M1)*(M2)/3r-2 = F/g 

(iii) F2 = G(2*M1)*(2M2)/r-2 = 4F, representing a force that has been multiplied by four.


17. How important is the gravitational law of universal gravitation?

Explanation:

Following are some key ideas that are consistent with the general law of gravitation: - (i) The force keeping us connected to the earth.

(ii) A planet's rotation around the sun.

(iii) This law explains why it is important to keep the atmosphere near the earth.


18. What is the rate of free fall acceleration?

Explanation:

As is common knowledge, g is equal to 9.8 m/s-2.

When a body falls because of the gravitational pull of the earth and accelerates as a result, this is known as free fall.


19. What do we name the attraction between an item and the earth?

Explanation:

Weight refers to the gravitational force exerted by the earth on an object.

It is equal to the product of the object's mass and the gravitational acceleration.

In mathematics, it can be expressed as,

Weight is equal to m*g times mg.


20. On the advice of one of his pals, Amit purchases a few grammes of gold at the poles. When they cross paths at the equator, he gives him the same. Will the friend accept the amount of gold that was purchased? Why not, then? [Hint: At the poles, the value of g is higher than at the equator]

Explanation:

F = GMm/r-2 is the formula for the universal law of gravitation.

The radius of the pole's curvature is smaller than the radius of the equator (rpole requator).

Newton's Second Law of Motion states that m*a pole = GMm W = mg (where m is the body's mass and g is the acceleration caused by gravity).


21. Why does a flat sheet of paper fall more slowly than one that is rolled up?

Explanation:

A sheet of paper will fall to the ground more slowly than one that has been rolled into a ball because:

(i) Because a sheet of paper has a larger surface area, there is more air resistance, which reduces speed.

(ii) A paper ball moves faster than a piece of plane paper because it has less surface area and, as a result, less air resistance.


22. The gravitational pull of the moon's surface is only 1/6 as powerful as that of the earth. How much does a 10 kilogramme object weigh in newtons on the moon and on earth?

Explanation:

The earth's gravity is 9.8 m/s-2.

Gravity on the moon is equal to one-sixth that of Earth (9.8/6 = 1.63 m/s-2)

The item on the moon weighs 10.63N (10*1.63).

the object's weight on Earth is equal to 10 * 9.8 = 98 N.


23. A ball is thrown 49 metres per second up in the air. Find the

(i) highest point it can reach and the (ii) time it will take to return to the earth's surface.

Explanation:

data provided

Starting speed, u, is 49 m/s.

Final speed v at the highest point equals zero.

g = -9.8 m/s2 is the acceleration caused by earth gravity (thus negative as ball is thrown up).

In accordance with the third equation of motion, 2gH = v2 - u2 2 (- 9.8) H = 0 - (49)2 - 19.6 H = - 2401 H = 122.5 m

Total time T is made up of the time it took to ascend and descend (Ta and Td, respectively).

Moreover, Td = 5 s, therefore T = Ta + Td T = 5 + 5 T = 10 s


24. A 19.6 m tall tower releases a stone into the air. Just before it hits the ground, calculate the object's final velocity.

Explanation:

data provided

initial speed u = 0

Tower height = overall length = 19.6 metres

g = 9.8 m/s2

Think about the third equation of motion.

v2 = u2 + 2gs

v2 = 0 + 2 × 9.8 × 19.6

v2 = 384.16

v = √(384.16) (384.16)

v = 19.6m/s

 

25. A stone is hurled vertically upward at a 40 m/s beginning speed. Determine the highest point the stone can reach using the formula g = 10 m/s2. How far has the stone travelled overall and what is its net displacement?

Explanation:

data provided

Starting speed, u, is 40 m/s.

g = 10 m/s2

Maximum height ultimate speed is 0.

Think about the third equation of motion.

V2 is equal to u2 - 2gs (negative as the object ascends).

0 = (40)2 – 2 x 10 x s

s = (40 x 40) / 20

Max height is 80 metres.

Distance total = s + s = 80 + 80

160 metres total distance

Overall displacement is equal to zero (the beginning and last points are identical).


26.Given that the Sun's mass is 2 1030 kg and the earth's mass is 6 1024 kg, calculate the gravitational force between the two bodies. 1.5 1011 metres separate the two on average.

Explanation:

data provided

The sun's mass is 2 1030 kg.

Earth's mass, ME, is 6 1024 kg.

constant of gravitation 6.67 x 10-11 N m2/kg2 = G

The typical distance is 1.5 1011 m.

Think about the Law of Gravitation.


27. A stone is permitted to fall from a tower that is 100 metres high while another stone is shot up vertically from the bottom at a speed of 25 metres per second. Determine where and when the two stones will collide.

Explanation:

data provided

(i) When the stone is flung from the top of the tower, initial velocity u' equals zero.

Travel distance = x

Time = t S = ut + 1/2 gt-2 x = 0 + 1/2 gt-2 x = 5 gt-2

...............(a)

(ii) The stone's initial velocity, u, is 25 m/s when it is flung upward.

Travel distance = (100 – x)

Time = t = ut + 1/2 gt-2 (100-x) = 25t- 1/2 *10*t-2 x = 100-25t + 5t-2

5t-2 = 100 -25t + 5t-2 is derived from equations (a) and (b).

...............(b) t = (100/25) = 4sec.

In 4 seconds, two stones will collide.

From (a) x = 5t2 = 5 x 4 x 4 = 80m.

Putting the value of x in (100-x)

= (100-80) = 20m


28. After six seconds, a vertically thrown ball returns to the thrower. Determine

 (a) the speed at which it was flung up,

 (b) the highest point it can reach, and

 (c) its position after four seconds.

Explanation:

Given data:

g = 10m/s2

a total of T = 6sec

Ta=Td=3 seconds (a) Final speed at maximum height is equal to zero.

Using the initial motion equation:

v = u - gta u = v - gta = 0 + 10 x 3 = 30 m/s

(b) 30*3 - 1/2*10*9 90 - 45 = 45m S = uta - 1/2gta-2

 (c) S = uta - 1/2 gta-2 s = 0 + 10 x 1 x 1 S = 5 m

The distance travelled in another 1sec = 5m.

As a result, point p will be 40m from the ground (45 - 5) in 4 seconds.

29. Which way does an object submerged in liquid experience buoyancy?

Explanation:

Vertically upward direction, as explained.


30. Why does a chunk of plastic that has been dropped into water rise to the surface?

Explanation:

Plastic has a lower density than water.

It floats and hence appears on the surface of the water when buoyant force exceeds weight and the net acceleration is upward.


31. A material weighing 50 g has a volume of 20 cm3. Will the substance float or sink if the density of the water is 1 g cm-3?

Explanation:

(Mass/Volume) Equals density

(50/20) = 2.5g/cm3 for density

Water has a density of 1 g/cm3.


32. A 500 g sealed packet's volume is 350 cm3. If the water has a density of 1 g cm-3, will the package float or sink? What volume of water will be displaced by this packet?

Explanation:

500/350 = 1.42 g/cm3 is the density of a sealed packet.

Because the sealed packet has a higher density than water, it will sink.

Taking into account Archimedes' Principle, force applied to the sealed packet = volume of displaced water.

350 cm3 is the amount of water moved.

Thus, the displaced water mass is given by: x V = 1 350

displaced water mass = 350g