Question 1 1 / -0
The escape velocity from Earth is 11.2 kms-1 . Another planet has mass 1000 times and radius 10 times that of Earth. The escape velocity at that planet will be
Question 2 1 / -0
If the distance between Earth and the sun becomes 4 times as much, then the time period of revolution will become
Solution
According to Kepler's third law, the square of orbital period, T, of a planet is proportional to the cube of its mean distance, R, from the sun.
T2 ∝ R
3 T ∝
T
1 /T
2 =
=
= 1 /
= 1/8
T
2 = 8 T
1
Question 3 1 / -0
The radius in kilometre, to which the present radius of Earth (R = 6400 km) is to be compressed, so that the escape velocity is increased to ten times, is
Solution
Escape velocity is given by
---- 1
For the second case, let the radius be R
1 .
---- 2
From 1 and 2, we have
R
1 = 64 km
Question 4 1 / -0
The apparent weight of a person inside a lift is 'w1 ', when lift moves up with a certain acceleration; and 'w2 ', when lift moves down with same acceleration. The weight of the person, when lift moves up with constant speed is:
Question 5 1 / -0
If the radius of Earth decreases by 1% and its mass remains the same, then the acceleration due to gravity
Solution
As we know, g =
Percentage error in value of 'g',
%
Hence,
%
+ve sign indicates the increase in the value of g.
Question 6 1 / -0
A satellite moves in an elliptical orbit about a planet maximum and minimum velocities are 3 x 104 m/s and 1 x 103 m/s. What is the minimum distance of satellite from planet if maximum distance is 4 x 104 km?
Question 7 1 / -0
If Earth is supposed to be a sphere of radius 'R' and if '
' is the value of acceleration due to gravity at a latitude of 30°, while 'g' is at the equator, the value of '(g -
)' is
Solution
The variation of acceleration due to gravity with latitude is given by,
Question 8 1 / -0
When the distance between Earth and the sun is halved, the duration of year will become
Question 9 1 / -0
If the Earth stops rotating, the value of g at the equator will
Solution
If the earth stops rotating, then the value of g at the equator increases and becomes equal to the value at poles. This is because, if the earth will stop rotating, then the equatorial bulge will vanish and earth will have a uniform radius and
since,
So, g is same as on the poles which is more than on equator. Hence, g will increase.
Question 10 1 / -0
An antenna is of height 500 m. What will be its range (Radius of the Earth is 6400 km)?
Solution
If 'd' is the range in which the transmission is reached and h is the height of the antenna,
Then,
Question 11 1 / -0
Three particles, each of mass 'm', are kept at the vertices of an equilateral triangle of side 'L'. The gravitational field at centre due to these particles is
Solution
As the distance of the mass from the centre is the same for all the masses, so the gravitational field intensity of each particle is the same. The given system is symmetric. Hence, the resultant gravitational field at the centre is zero.
Question 12 1 / -0
The period of revolution of a planet around sun is 27 times that of Earth. The ratio of radius of planet's orbit to the radius of Earth's orbit is
Question 13 1 / -0
Directions:
Solution
In the satellite apparent value of 'g' = 0 so the time period of the pendulum approaches to infinity.
Question 14 1 / -0
If the value of escape velocity on a certain planet is 2 km/s, the value of orbital speed for a satellite orbiting close to its surface will be
Question 15 1 / -0
A satellite is orbiting around the earth with orbital radius 'R' and time period 'T'. The quantity which does not depend on the size of satellite is
Question 16 1 / -0
What is ratio of gravitational mass and inertial mass?
Question 17 1 / -0
If a new planet is discovered rotating around the sun with the orbital radius double of that of Earth, what will be its time period (in earth's days)?
Solution
Using
If T
P is the time period of the planet and T
e is the time period of the earth then we have
T
P = 1033 days
Question 18 1 / -0
Astronauts look down on the Earth's surface from a space ship parked at an altitude of 500 km. They can resolve objects of the Earth of the size_____ (It can be assumed that the pupil's diameter is 5 mm and wavelength of light is 500 nm).
Question 19 1 / -0
Two balls, each of radius R and of equal mass and density, are placed in contact. Then, the force of gravitation between them is proportional to
Solution
Let the mass of each ball be M and the density of the material be d. If the two spheres are in contact with each other, then the distance between the centres of both the spheres will be 2R.
Force between the two spheres
And
Then,
Question 20 1 / -0
A person is sitting in a lift accelerating upwards. The measured weight of the person will be
Question 21 1 / -0
Acceleration due to gravity 'g' for a body of mass 'm' is proportional to (Radius of Earth = r, Mass of Earth = M)
Solution
Acceleration due to gravity g =
Question 22 1 / -0
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius 'R' around the sun will be proportional to:
Question 23 1 / -0
The change in the value of 'g' at a height 'h' above the surface of Earth is the same as at a depth 'd' below the surface of Earth. When both 'd' and 'h' are much smaller than the radius of Earth, then which of the following expressions is correct?
Question 24 1 / -0
The Earth moves in an elliptical orbit with the sun S at one of foci as shown in the figure. Its rotational kinetic energy is maximum at the point
Solution
Key Idea: In planetary motion, angular momentum remains conserved.
The earth revolves around the sun once in a year. In order to find the rotational kinetic energy about the sun, we may treat the earth as a point mass, of moment of inertia I. If
is angular velocity of earth, then
K
rot =
I
2 In planetary motion, angular momentum remains conserved. At A, the moment of inertia is least, so angular speed is maximum. So, at A, rotational kinetic energy is maximum.
Question 25 1 / -0
A closed organ pipe of length 20 cm is sounded with tuning fork in resonance. What is frequency of tuning fork? (v = 332 m/s)
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