Some basics and Universal law of Gravitation 9th class(lec 1)

 video lecture for Some basics and the Universal law of Gravitation

Question 1: If the distance between two objects is halved, how will the gravity between them change?

Question 2: The gravitational force on all objects is directly proportional to their mass. Then why doesn't a heavy object fall faster than a light object?

Question 3: What will be the magnitude of the gravitational force between the earth and an object of mass  `1 kg` placed on its surface? (Earth's mass is `6\times10^{24} kg` and Earth's radius is `6.4\times10^{6} m`.)

Question 4: The gravitational force between two objects is `F`. If masses of both objects are halved without changing distance between them, then the

gravitational force would become

(a) `\frac{F}{4}`

(b) `frac{F}{2}`

(c) `F`

(d) `2 F`

Question 5: A boy is whirling a stone tied with a string in an horizontal circular path. If the string breaks, the stone

(a) will continue to move in the circular path

(b) will move along a straight line towards the centre of the circular path

(c) will move along a straight line tangential to the circular path

(d) will move along a straight line perpendicular to the circular path away from the boy

Question 6: In the relation `F=G\frac{Mm}{d^{2}}`, the quantity  `G`

(a) depends on the value of g at the place of observation

(b) is used only when the earth is one of the two masses

(c) is greatest at the surface of the earth

(d) is universal constant of nature

Question 7: Law of gravitation gives the gravitational force between

(a) the earth and a point mass only

(b) the earth and sun only

(c) any two bodies having some mass

(d) two charged bodies only

Question 8: The value of quantity `G` in the law of gravitation

(a) depends on mass of earth only

(b) depends on radius of earth only

(c) depends on both mass and radius of earth

(d) is independent of mass and radius of the earth

Question 9: Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be

(a) `1/4` times

(b) `4` times

(c) `1/2` times

(d) unchanged

Question 10: The force of attraction between two unit point masses separated by a unit distance is called

(a) gravitational potential

(b) acceleration due to gravity

(c) gravitational field

(d) universal gravitational constant

Question 11: An apple falls from a tree because of gravitational attraction between the earth and  apple. If `F`, is the magnitude of force exerted by the earth on the apple and `F_{2}` is the magnitude of force exerted by apple on earth, then

(a) `F_{1}` is very much greater than `F_{2}`

(b) `F_{2}` is very much greater than `F_{1}`

(c) `F_{1}` is only a little greater than `F_{2}`

(d) `F_{1}` and `F_{2}` are equal

Question 12: What is the source of centripetal force that a planet requires to revolve around the sun? On i what factors does that force depend?

Question 13: State Newton’s universal law of gravitation

Question 14: State Kepler’s 1st law of planetary motion

Question 15: State Kepler’s 2nd law of planetary motion

Question: 16: State Kepler’s 3rd law of planetary motion.

Question 17: Weights of two bodies are `20 N` and `30 N`. If they are separated by a distance of `2 m`, what is the force of gravitation acting between them? (`g=10ms^{-2}`)

a) `10.4\times10^{-11}N`

b) `9.4\times10^{-11}N`

c) `10.4\times10^{-10}N`

d) `10.4\times10^{11}N`

Question 18: If the distance between the Earth and the sun shrinks 

to half the present distance, then find the new duration of the year.

a) `139` days

b) `149` days

c) `129` days

d) `119` days

Question 19: The mean distance of two planets `A` and `B` from the sun 

is `2` and `4` times the distance of the Earth from the sun, 

respectively. Find the ratio of the time taken by the two 

planets to make one revolution around the sun.

a) `1 : 2\sqrt{2}`

b) `1 :2` 

c) `3 :2`

d) `2\sqrt{2}  : 1`

Question 20: Give two practical examples of the equilibrium of bodies in our daily life.

Question 21: If the gravitational force between two bodies of

masses `10 kg` and `100 kg` separated by a distance `10 m`

is `6.67\times10^{-10} N`, then the force between the given

masses would be ________ `N` if they are placed in a

geostationary satellite without change in the distance

between them.

(a) `3.335\times10^{-10}`  

(b) `3.335\times10^{-11}`

(c) `6.67\times10^{-10}`  

(d) `6.67\times10^{-11}`

Question 22: . If the acceleration due to gravity on a planet is

`6.67 m s^{−2}`  and its radius is `4\times10^{6}m`, then the mass

of the planet is _____.

(a) `16\times10^{23} kg`  

(b) `726\times10^{23} kg`

(c) `16\times10^{24} kg`

(d) `26\times10^{24} kg`

Question 23: What is the relation between the period of rotation

(`R_{T}`) and period of revolution (`R_{V}`) of moon?

(a) `R_{T} = R_{V}`  

(b) `R_{V} > R_{T}`

(c) `R_{V} < R_{T}`  

(d) No relation exists

Question 24: Which of the following graphs is true for the motion

of a satellite revolving round the Earth. (`‘T’` is the

time period of a satellite and ‘r’ is the distance of the

satellite from the Earth).

Question 25: If the force between bodies of mass `2 kg` and `4 kg`, separated by a distance `4 m`, is `3.335\times10^{-11} N`, then the force between them if the bodies are shifted to the moon without altering the distance between them will be _____.

(a) `0.03335 N`

(b) `3.335\times10^{-11}N` (c) `5.558\times10^{-12} N`

(d) `6.28\times10^{-12} N`

Question 26: According to Newton’s Universal law of gravitation, the gravitational force between two bodies is

(a) always attractive and depends on their masses. (b) depends on the distance between them. (c) does not depend on the medium between the bodies.

(d) All the above

Question 27: According to Kepler’s second law of planetary

Motion,

(a) the line joining the centers of a planet’s orbit and

the planet covers equal areas in equal intervals of

time.

(b) the line joining the centers of sun and the planet

covers equal area in equal intervals of time.

(c) a planet covers equal distances along its orbit in

equal intervals of time.

(d) area swept by the average radius of orbit of each

planet in the solar system is equal

Answer Key

Q1:   `F∝\frac{1}{r^{2}}`

So when the distance between two objects is halved, the force of gravity will be quadrupled.

Q2:  A heavier object does not fall faster than a lighter object due to the resistance of the object. Air resistance to a light object is greater than that to a heavy object.

Q3:  Soulation:       `m_{1}=1kg`

                    `m_{2}=6\times10^{24}kg`

                    `r=6.4\times10^{6}m`

                    `G=6.67\times10^{-11}Nm^{2}kg^{-2}`

                    

                    `F=G\frac{m^{1}m^{2}}{r^{2}}`

                   `F=\frac{6.67\times10^{-11}\times(1)\times6\times10^{24}kg}{6.4\times10^{6}}`

                    

                    `F=9.77 N`

Q4:   Solution:

(a): Let the masses of two objects be `m_{l}` and `m_{2}` placed at d distance apart.

So, `F=G\frac{m_{1}m_{2}}{d^{2}}`

When the masses of two objects are halved,

`F'=G\frac{\frac{m_{1}}{2}\times\frac{m_{2}}{2}}{d^{2}} =G\frac{m_{1}m_{2}}{4d^{2}}=\frac{F}{4}`

Q5:  (c) If the string breaks, the force that was causing it to move along a circular path, i.e., centripetal force is no longer there, so the stone will move along a straight line tangential to the circular path.

Q6:   (d) In the relation `F=G\frac{Mm}{d^{2}}`, the quantity `G` is universal constant of nature.

Q7:  (c) Law of gravitation gives the gravitational force between any two bodies having some mass as it is a universal law.

Q8:   (d) The value of quantity `G` in the law of gravitation is independent of mass and radius of the earth.

Q9:  So, the gravitational force between the two particles will become 4 times.

Q10:    Solution:

(d)  `F=G\frac{m_{1}m_{2}}{d^{2}}`

`F = G`, i.e., the force of attraction between two unit point masses separated by a unit distance is universal gravitational constant.

Q11:   Solution:

(d) `F_{1}` and `F_{2}` are equal as Newton’s law of gravitation obeys the Newton’s third law of motion, i.e., if an object exerts a force on another object, then the second object exerts an equal and opposite force on the first object.

Q12:   Solution:

A planet requires centripetal force to revolve around the sun which is provided by the gravitational force of sun on the planet.

As `F=G\frac{M_{s}M_{p}}{r^{2}}` the force depends on the mass of sun (`M_{s}`), mass of planet (`M_{p}`) and the distance between the two `(r)`.

Q13:   Newton's Law of Universal Gravitation states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

Q14:    each planet's orbit about the Sun is an ellipse. The Sun's center is always located at one focus of the orbital ellipse. The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit.

Q15:  a planet moves in its ellipse so that the line between it and the Sun placed at a focus sweeps out equal areas in equal times.

Q16:  the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. 

Q17:   (a),    Q18:     (c),   Q19:   (a)

Q20  A book kept on a table at rest. A car moving with a constant velocity.

Q21:    (c),   Q22:    (a),   Q23:    (a),   Q24:     (c), Q25:    (b), Q26:   (d), Q27:    (b).