1. Complete the following statements.
[1 Mark each]
i. Sir Isaac Newton gave his laws of motion, equations of motion and theory of gravity in his book___________.ii. The orbit of a planet is an ellipse with the Sun at one of the____________.
iii. For bodies which are not spherical or having an irregular shape, the direction of the force is along the line joining their____________.
iv. The centre of a mass of any object having uniform density is at its_________.
V. According to Newton's first law, mass is the measure of_________ of an object.
vi. For an object at infinite distance from the earth, the value of acceleration due to gravity (g) is___________.
vii. Mass is a_____________ quantity.
viii. True free fall is possible only in__________
ix. For a freely falling body, we can write Newton's third equation of motion as_______________
x. An object going vertically upwards will be free from the gravitational influence of the earth, if its initial velocity is equal to ______________of the earth.
xi. In a space station, the value of g is only____________ percent less than its value on the surface of the earth.
Answers:
i. Principia.
ii. foci.
iii. centres of mass
iv. centroid.
v. inertia
vi. zero
vii. scalar
viii. vacuum
ix. v^2 = 2 gs
x. escape velocity
xi. eleven
2. Select the appropriate options and complete
the following paragraph.
[3 Marks]
(velocity, independent, initial velocity,dependent, gravity, friction, final velocity,
direction)
The motion of any object under the influence of
the force of_________alone is called as free fall.
During free fall, there will be no change in the ___________ of motion of the object. But there will be a change in the magnitude of___________ of the object due to the gravitational pull of the earth. The acceleration that an object experiences during free fall is___________of the mass of the object undergoing motion. When a body is dropped freely from a height, its_____________ is zero. Whereas when a body is thrown vertically upwards, its _____________ is zero.
Answer:
The motion of any object under the influence of the force of gravity alone is called as free fall. During free fall, there will be no change in the direction of motion of the object. But there will be a change in the magnitude of velocity of the object due to the gravitational pull of the earth. The acceleration that an object experiences during free fall is
independent of the mass of the object
undergoing motion. When a body is dropped freely from a height, its initial velocity is zero. Whereas when a body is thrown vertically upwards, its final velocity is zero.
Choose the correct alternative (1 Mark each)
1. A boy is whirling a stone tied to a string in a horizontal circular path. If the string breaks, the stone_______________
(A) will move along a straight line towards
the centre of the circular path.
(B) will move along a straight line
perpendicular to the circular path away
from the boy.
(C) will move along a straight line tangential to the circular path.
(D) will continue to move in circular path.
2. 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
3. The force of attraction between two unit point masses separated by a unit distance equals. ___________
(A) gravitational potential.
(B) acceleration due to gravity.
(C) gravitational field.
(D) universal gravitational constant.
4. According to Newton's law of gravitation, for two objects kept at a distance d from each other, if the distance between the objects is doubled, then the force between the two objects ___________
(A) increases by a factor of 4
(B) decreases by a factor of 4
(C) decreases by a factor of 2
(D) increases by a factor of 2
5. The tidal waves in the sea are primarily due to gravitational effect of
(A) earth on the sea.
(B) Sun on the earth.
(C) earth on the moon.
(D) moon on the earth.
6. The value of acceleration due to gravity_____________
(A) is same at the equator and poles.
(B) is least at the poles.
(e) is least at the equator.
(D) is maximum at the centre of the earth.
7. According to Newton's first law of motion, higher the mass____________ is the inertia.
(A) lower
(B) higher
(C) zero
(D) double
8. A spherical planet far out in space has a mass M,and diameter D. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity equal to
(A) GM/D; (B) 4mGM/DZ
(C) 4GM/D (D) GmM/D
9. The value of g on moon is 1/6 of its value on the. earth. If a person weighs 14 N on the moon's. surface,then the weight of the person on earth's. surface is ____________
(A) 96 N
(B) 84 N
(C) 62 N
(D) 54 N
10. What is the gravitational potential energy of an object located 20,000 m above the earth's surface?
(A) U=-GMm/(20 km +RE)
(B) U=-GMm/(20,000 km + Rg)
(C) U=-GMm/RE
(D) U= GMm/(RE-20 km)
Answers:
1. (C)
2. (C)
3. (D)
4. (B)
5. (D)
6. (C)
7. (B)
8. (C)
9. (B)
10. (A)
Name the following [1 Mark each]
1. Force which is directed towards the centre of the circle (centre seeking).
2. Amount of matter present in an object.
3. Force with which the earth attracts an object.
4. Scientist who was appointed as the royal mathematician in place of Brahe.
5. Observatory constructed by scientists to detect the gravitational waves emitted by astronomical sources.
Answers:
1. Centripetal force
2. Mass
3. Weight of the object.
4. Johannes Kepler
5. LIGO-Laser Interferometric Gravitational
Wave Observatory
Right or wrong.
If wrong, write the correct sentence
[1 Mark each]
1. Two planets move around the Sun. The periodic times and the mean radii of the orbits are T1, T2, and r1, r2, respectively. Then the ratio T1/T2, is equal to (r1/r2).^(2/3)2. Gravitational force is the strongest force in nature.
3. According to Newton's third law of motion, a force acting on a body results in its acceleration.
4. Due to its rotation, the earth is flatter at the equator and bulges at the poles.
5. As we go above the earth's surface, the value of acceleration due to gravity increases.
6. The acceleration due to gravity at a given point on the earth is the same for all the objects.
7. The moon and the artificial satellites are all in free fall.
8. The escape velocity is same for different planets.
Answers:
1. Wrong
Two planets move around the Sun. The periodic
times and the mean radii of the orbits are T1, T2,
and r1/r2, rrespectively. Then the ratio T/T2 is
equal to (r1/r2)^(3/2)
2. Wrong
Gravitational force is the weakest force in nature.
3. Wrong
According to Newton's second law of motion, a
force acting on a body results in its acceleration.
4. Wrong
Due to its rotation, the earth bulges at the
equator and is flatter at the poles.
5. Wrong
As we go above the earth's surface, the value of
acceleration due to gravity decreases.
6. Right
7. Right
8. Wrong
The escape velocity is different for different planets.
[Hint: Escape velocity is given as,
Vesc= / - 2GM where M is mass and R is radius of the planet which is not same for different planets.]
Odd one out. [1 Mark each]
1. Force, acceleration due to gravity, weight, mass.
2. v=gt, h= gt, v=u + at, v2 = 2gh
3. The orbit of a planet is an ellipse, line joining the planet and the sun sweeps equal areas in equal intervals of time, F = Gm1m2/r^2, T^2αR^3
Answers:
1. Mass
Mass is a scalar while other are vectors
2. v=u+ at
v = u + at is the fundamental kinematical
equation of motion while others are kinematical
equations for a freely falling body.
3. F= Gm1m2/r^2
F = Gm1m2/r^2, is Newton's law of gravitation while others are Kepler's laws of planetary motion.
Complete the analogy [1 Mark each]
1. Gravitational constant: scalar quantity ::
acceleration due to gravity : _____________
2. Kinetic energy of a body of mass m on the surface of the earth: -1/2mv^2esc : kinetic energy of a body. of mass m at infinite distance from earth:____________
3. Kepler's first law: orbit of a planet is an ellipse
::____________ :T^2αr^3
(T is orbital period of revolution of a planet and r is the mean distance of the planet from sun.)
4. Increase in altitude: value of g decreases :: at the centre of the earth:________________
Answers:
1. vector quantity
Gravitational constant is a scalar quantity and acceleration due to gravity is a vector quantity.
2. zero
Kinetic energy of a body of mass m on the surface of the earth is 1/2mv^2esc. While kinetic energy of a body of mass m at infinite distance from earth is zero.
3. Kepler's third law
Orbit of a planet is an ellipse is Kepler's first law while T?aris Kepler's third law.
4. value of g is zero.
Value of g decreases with increase in altitude while the value of g becomes zero at the centre of the earth.
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