An object of mass 1 KG is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [lf, g = 10 ms^{-1} and radius of earth = 6400 km ]
1 ) 48 MJ
2 ) 24 MJ
3 ) 36 MJ
4 ) 12 MJ
Question 2 :
Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is - (consider radius of earth RE = 6400 km and g on earth 10 m/s^{2})
1 ) 1200 km
2 ) 1600 km
3 ) 3200 km
4 ) 4800 km
Question 3 :
If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :
1 ) decrease by 2%
2 ) decrease by 4%
3 ) increase by 2%
4 ) increase by 4%
Question 4 :
Two satellites A and B, having masses in the ratio 4 : 3, are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is :
1 ) 9:16
2 ) 16 : 9
3 ) 1 : 1
4 ) 4 : 3
Question 5 :
A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be : (Take radius of earth :
1 ) 800 km
2 ) 1600 km
3 ) 2133 km
4 ) 4800 km
Question 6 :
The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be : (Radius of earth =1600 km) A
1 ) 1%
2 ) 3%
3 ) 4%
4 ) 0.50%
Question 7 :
The length of a seconds pendulum at a height h = 2R from earth surface will be : (Given R = Radius of earth and acceleration due to gravity at the surface of earth, g π^{2} ms^{-2})
1 ) 2/9 m
2 ) 4/9 m
3 ) 8/9 m
4 ) 1/9 m
Question 8 :
Three identical particles A, B and C of mass 100 kg each are placed in a straight line with AB BC 13 m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13 m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately :
1 ) 21 G
2 ) 100 G
3 ) 59 G
4 ) 42 G
Question 9 :
The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3p and 5p respectively. The ratio of their acceleration due to gravity is :
1 ) 9:4
2 ) 9:8
3 ) 9:10
4 ) 2:5
Question 10 :
The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be
1 ) 40 hours
2 ) 36 hours
3 ) 30 hours
4 ) 25 hours
Question 11 :
The escape velocity of a body on a planet 'A' is 12 km/s. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :
1 ) 12 km/s
2 ) 24 km/s
3 ) 36 km/s
4 ) 6 km/s
Question 12 :
Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be :
1 ) 2F/9
2 ) 16F/9
3 ) 8F/9
4 ) F
Question 13 :
Given below are two statements : Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below.
1 ) Both Statement I and Statement II are true
2 ) Both Statement I and Statement II are false
3 ) Statement I is true but Statement II is false
4 ) Statement I is false but Statement II is true
Question 14 :
The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).
1 ) g/2
2 ) g/4
3 ) g/3
4 ) g/9
Question 15 :
A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :
1 ) -60 G
2 ) 2 G
3 ) -20 G
4 ) -4 G
Question 16 :
Inside a uniform spherical shell : (1) the gravitational field is zero (2) the gravitational potential is zero (3) the gravitational field is same everywhere (4) the gravitational potential is same everywhere (5) all of the above Choose the most appropriate answer from the options given below :
1 ) (1), (3) and (4) only
2 ) (5) only
3 ) (1), (2) and (3) only
4 ) (2), (3) and (4) only
Question 17 :
1 ) b
2 ) c
3 ) d
4 ) a
Question 18 :
If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately : [Take g = 10 ms^{-2}, the radius of earth, R = 6400 × 10 ^{3} m, Take π = 3.14]
1 ) 84 minutes
2 ) 1200 minutes
3 ) 60 minutes
4 ) does not change
Question 19 :
The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 9R is :
1 ) 9 T
2 ) 27 T
3 ) 12 T
4 ) 3 T
Question 20 :
Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight? (Assume radius of earth is 6400 km)
1 ) 158.2 m
2 ) 79.1 m
3 ) 19.77 m
4 ) 39.55 m
Question 21 :
1 ) 36 : 25
2 ) 41 : 50
3 ) 50 : 41
4 ) 25 : 36
Question 22 :
Consider two satellites S1 and S2 with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellite S2 is :
1 ) 1 : 4
2 ) 8 : 1
3 ) 2 : 1
4 ) 1 : 8
Question 23 :
The value of the acceleration due to gravity is g_{1} at a height h = R/2 (R = radius of the earth) from the surface of the earth. It is again equal to g_{1} at a depth d below the surface of the earth. The ratio d/R equals :
1 ) 5/9
2 ) 1/9
3 ) 7/9
4 ) 4/9
Question 24 :
1 ) 2/3
2 ) 1/6
3 ) 1/2
4 ) 1/3
Question 25 :
A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms–2 at the north pole and the radius of the earth = 6400 km) :
1 ) 194.32 N
2 ) 195.66 N
3 ) 195.32 N
4 ) 194.66 N
Question 26 :
The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the planet is 1/9 th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)
1 ) R/9
2 ) R/2
3 ) R/3
4 ) R/4
Question 27 :
A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet? [Given; Mass of planet = 8 × 10 ^{22} kg, Radius of planet = 2 × 10 ^{6} m, Gravitational constant G = 6.67 × 10 ^{-11} Nm ^{2} kg ^{2}]
1 ) 13
2 ) 9
3 ) 17
4 ) 11
Question 28 :
The value of acceleration due to gravity at Earth's surface is 9.8 ms ^{–2}. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms ^{–2}, is close to : (Radius of earth = 6.4 × 10 ^{6} m)
1 ) 1.6 × 10 ^{6} m
2 ) 9.0 × 10 ^{6} m
3 ) 6.4 × 10 ^{6} m
4 ) 2.6 × 10 ^{6} m
Question 29 :
A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :-
1 ) E/32
2 ) E/16
3 ) E/4
4 ) E/64
Question 30 :
A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be :