Gravity Questions 9th class (lec 5)

video lecture for  Gravity question 

Question 1: Suppose gravity of earth suddenly becomes zero, then in which direction will the moon begin to move if no other celestial body affects it?

Question 2: Calculate the average density of the earth in terms of `g`, `G` and `R`.

Question 3: The earth is acted upon by gravitation of sun, even though it does not fall into the sun. Why?

Question 4: How does the weight of an object vary with respect to mass and radius of the earth? In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times its present value, then how would the weight of any object on the surface of the earth be affected?

Question 5: How does the force of attraction between the two bodies depend upon their masses and the distance between them? A student thought that two bricks tied together would fall faster than a single one under the action of gravity. Do you agree with his hypothesis or not? Comment.

Question 6: Define an artificial satellite

Question 7: What is a geostationary satellite and what is its time Period?

Question 8: Where does the `C.G.` of regular shaped bodies lie?

Question 9: A spring balance measures the _____ of a body. Question 10: Time period of revolution of a planet is `1000` days. If the distance between the sun and planet is altered such that `8000` days on it will make one year, then this altered distance is ______ the original distance. a) `1/2` b) `1/4` c) `1/3` d) `3/2`

Question 11: What do you understand by the position of a body?

Question: 12: Irregularity in the motion of a star is known as a _________

Question 13: Define mass, weight and centre of gravity. Question 14: Define geotropism.

Question 15: What is acceleration due to gravity? Question 16: Define the time period of a satellite Question 17: How does altitude affect `‘g’`? Question 18: The time period of a geostationary satellite is equal to ________ hours.

Question 19: Compare mass and weight.

Question 20: When a spring balance, which showed a reading of `30` divisions on earth, is taken to the moon, will show (for the same body)

(a) `180` divisions.

(b) `6` divisions. (c) `150` divisions.

(d) `5` divisions.

Question 21: The centre of gravity `C.G.` of the bob of a given simple pendulum is at position `‘x’` on earth. What is its new position on the surface of the moon?

(a) It remains at the same position `‘x’`. (b) It is above the position `‘x’` (c) It is below the position `‘x’` (d) It shifts towards surface of the bob.

Question 22: One revolution of a given planet around the sun is `1000` days. If the distance between the planet and the sun is made `¼th` of original value, then how many days will make one year?

(a) `180` days

(b) `400` days (c) `125` days

(d) `250` days

Question 23: The length of a seconds pendulum on the surface of the Earth is `100 cm`. Find the length of the seconds pendulum on the surface of the moon. `(g_{M}=16g_{E})`

(a) `1.66 m`

(b) `16.6 cm` (c) `33.2 cm`

(d) `3.32 m`

Question 24: Which is not correct about escape velocity?

(a) Escape velocity of a body depends on its mass. (b) Escape velocity of a body is greater than its orbital velocity (c) Escape velocity of a body is different on different Planets (d) Escape velocity of a body on a planet depends on the mass of the planet.

Direction for questions `25` to `31` State whether the following statements are true or false. Question 25: The weight of a body on the surface of moon is 1/6th of that on the Earth’s surface. It is because acceleration due to gravity on the surface of moon is six times that on the surface of the Earth.

Question 26: The dimensional formula of universal gravitational constant `‘G’` is `[M^{−1}L^{3}T^{−2}]`.

Question 27: Heliocentric theory was proposed by Tyco Brahe.

Question 28: If a heavenly object like an asteroid or a planetoid revolving around the sun moves into an orbit of smaller radius, its speed increases.

Question 29: Acceleration due to gravity vanishes at an altitude equal to half the radius of the Earth.

Question 30: For any given body, the centre of the mass of a body always coincides with its centre of gravity.

Question 31: The direction of motion of an artificial satellite revolving in a geostationary orbit is opposite to the direction of the Earth’s rotation.

Direction for questions `32` to `38` Fill in the blanks

Question 32: The ratio of ‘g’ on two known planets `‘A’` and `‘B’` is `x : y`. If two identical bodies are projected with the same velocity on these planets, then the ratio of their time of descent is _______. (Neglect atmospheric resistance). Question 33: According to Kepler’s laws of planetary motion, the orbits of planets are of ___________shape. Question 34: Two satellites of identical masses orbit the Earth at different heights. The ratio of their distances from the centre of earth is `d : 1` and the ratio of the acceleration due to gravity at those heights is `g : 1`. Then the ratio of their orbital velocities is __________. Question 35: A football floating on the waves of ocean water is an example of _______ equilibrium. Question 36: Newton’s inverse square law is deduced from Kepler’s ___________ law of planetary motion. Question 37: All the particles of a shuttle cock execute complicated motion, but its ________describes the simplest path when it is projected. Question 38: The law that helps in determining the masses of the stars present in a double star is ________.

Directions for question `39` Match the entries given in Column `A` with appropriate ones in Column `B`.

Answer Key

Q1: The circular motion of the moon around earth is due to the centripetal force provided by gravitational force of earth. Therefore,

when gravity of earth suddenly becomes zero, the moon will begin to move in a straight line in the direction in which it was moving at that instant. That is the moon will move along the tangent to the circular orbit at that instant.

Q2: Solution

Let the earth be a sphere of redias `R`

Now density `ρ=MV`

From newton's law of gravitation 

`g=G\frac{M}{R^{2}}`  or `M=\frac{gR^{2}}{G}`

Volume of earth, `V=\frac{3}{4\piR^{3}}`

density=`\frac{gR^{2}}{G}\times\frac{3}{4\piR^{3}}`

`=\frac{3g}{4\piRG}`

Q3: If the sun's gravitational force on earth is utilized in providing its centripetal force required for revolution around the sun. Hence, the earth does not fall into the sun.

Q4: Solution:

Weight of an object of mass m, `W=md`

`=G\frac{Mm}{R^{2}}`

Weight varies directly with respect to mass of earth, `W∝ M` and inversely with respect to radius of earth, `W∝\frac{1}{R^{2}}`

When diameter of the earth becomes half, radius of earth also becomes half and mass becomes `4` times of its initial value, then

         `W'=G4\frac{Mm}{(R/2)^{2}}=16G\frac{Mm}{R^{2}}=16W`

i.e., weight will become `16` times its initial value.

Q5: Solution:

From Newton’s law of gravitation, force of attraction between two bodies is directly proportional to the product of their masses, and inversely proportional to the square of distance between their centres i.e., `F∝\frac{m_{1}m_{2}}{d^{2}}` Student’s hypothesis is wrong. As acceleration due to gravity is independent of the mass of the falling body, therefore, the two bricks tied together, falls with same speed as the single one to reach the ground at the same time under the action of gravity.

Q6: An electronic device that is sent into space and moves around the earth or another planet for a particular purpose

Q7: one of the artificial satellites, which revolves around Earth's equator above `22,236` miles in a geostationary orbit.

Q8: Normally the center of gravity of a human is about an inch below the navel in the center of the body.

Q9: Weight, Q10: (b)

Q11: The positioning of the body when it is standing upright and facing forward with each arm hanging on either side of the body, and the palms facing forward.

Q12: wobble.

Q13: The center of mass is defined as the distribution of mass in space.

In center of mass, the objects are weighed and divided according to their masses. On the other hand, the center of gravity is defined as a point at which the object acts in response to gravity.

Q14: The growth of the parts of plants in response to the force of gravity. The upward growth of plant shoots is an instance of negative geotropism ; the downward growth of roots is positive geotropism.

Q15: The acceleration gained by an object due to gravitational force.

Q16: The time it takes it to make one full orbit around an object.

Q17: The gravitational acceleration decreases with altitude.

Q18: `24`

Q19: Mass is the amount of matter in a material, while weight is a measure of how the force of gravity acts upon that mass.

Q20: (d), Q21: (a), Q22: (c), Q23: (b), Q24: (a),

Q25: False, Q26: True, Q27: False, Q28: True, Q29: False, Q30: False, Q31: False,

Q32: `y : x` Q33: elliptical Q34: dg Q35: neutral Q36: third Q37: center of mass Q38: Newton’s law of gravitation,

Q39: A : e B : d C : i D : c E : b F : j G : a H : g I : f J : h