R4RIN – MCQs, Mock Tests | IIT JEE IIT JEE Gravitation part1

If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth the height of the satellite above the surface of the earth is:

1. 2R
2. R/2
3. R
4. R/4

✅ Correct Answer: 3

The time period of a simple pendulum at the centre of earth is:

1. zero
2. infinite
3. less than zero
4. none of these

✅ Correct Answer: 2

A satellite is orbiting very close to planet. Its time period depends only upon:

1. density of the planet
2. mass of the planet
3. radius of the planet
4. mass of the satellite

✅ Correct Answer: 1

The minimum energy required to launch a m kg satellite from earths surface in a circular orbit at an altitude of 2R where R is the radius of earth will be:

1. 3mgR
2. 5/6 mgR
3. 2mgR
4. 1/5mgR

✅ Correct Answer: 2

If suddenly the gravitational force of attraction between earth and a satellite revolving around it becomes zero then the satellite will:

1. continue to move in its orbit with same velocity
2. move tangentially to the original
3. orbit with the same velocity
4. become stationary in its orbit

✅ Correct Answer: 2

Mark correct option or options.

1. Only equatorial orbit are stable for a satellite
2. Escape velocity does not depend upon angle of projection
3. A communication satellite rotates in a direction from west to east
4. All of the above

✅ Correct Answer: 4

A particle hanging from a massless spring stretches it by 2 cm at earths surface. How much will the same particle stretch the spring at height 2624 km from the surface of earth? (Radius of earth = 6400 km)

1. 1 cm
2. 2 cm
3. 3 cm
4. 4 cm

✅ Correct Answer: 1

The gravitational potential difference between the surface of a planet and a point 20 m above it is 16 J/kg. Then the work done in moving a 2 kg mass by 8 m on a slope 60 degree from the horizontal is:

1. 11.1 J
2. 5.55 J
3. 16 J
4. 27.7 J

✅ Correct Answer: 1

A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The time period of the second satellite is larger than that of the first one by approximately:3.0%

1. 0.50%
2. 1.50%
3. 1%
4.

✅ Correct Answer: 2

Two spherical bodies the mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only then the distance covered by the smaller body just before collision is:

1. 2.5 R
2. 4.5 R
3. 7.5 R
4. 1.5 R

✅ Correct Answer: 3

If the radius of earth decreases by 10% the mass remaining unchanged what will happen to the acceleration due to gravity?

1. Decreases by 19%
2. Increases by 19%
3. Decreases by more than 19%
4. Increases by more than 19%

✅ Correct Answer: 4

Average density of the earth:

1. does not depend on g
2. is a complex function of g
3. is directly proportional to g
4. is inversely proportional to g

✅ Correct Answer: 3

In the above question if the satellite is stopped suddenly in its orbit and allowed to fall freely onto the earth the speed with which it hits the surface of the earth is: (Assume g = 10 m/second square and R = 6400 km)8 km/s2 km/s6 km/s

1. 4 km/s
2. 8 km/s
3. 2 km/s
4. 6 km/s

✅ Correct Answer: 2

How the gravitational constant will change if a brass plate is introduced between two bodies?

1. No change
2. Decreases
3. Increases
4. No sufficient data

✅ Correct Answer: 1

Two earths satellites are revolving in the same circular orbit round the centre of the earth. They must have the same:

1. mass
2. angular momentum
3. kinetic energy
4. velocity

✅ Correct Answer: 4

The time period of a satellite of earth is 5 h. If the separation between the earth and the satellite is increased to 4 times the previous value the new time period will become:

1. 10h
2. 80h
3. 40h
4. 20h

✅ Correct Answer: 3

If the radius of the earth reduces by 4% density remaining the same then the escape velocity will:

1. increase by 4%
2. increase by 2%
3. decrease by 4%
4. decrease by 2%

✅ Correct Answer: 3

The time period of an earths satellite in circular orbit is independent of:

1. the mass of the satellite
2. radius of its orbit
3. both the mass and radius of the orbit
4. neither the mass of the satellite nor the radius of its orbit

✅ Correct Answer: 1

When a satellite going round the earth in a circular orbit of radius r and speed v loses some of its energy then r and v change as:

1. r and v both will increase
2. r and v both will decrease
3. r will decrease and v will increase
4. r will increase and v will decrease

✅ Correct Answer: 1

When a satellite going round the earth in a circular orbit of radius r and speed v loses some of its energy then r and v change as:

1. r and v both will increase
2. r and v both will decrease
3. r will decrease and v will increase
4. r will increase and v will decrease

✅ Correct Answer: 4

The time period of artificial satellite in a circular orbit of radius R is T. The radius of the orbit in which time period is 8T is:

1. 2R
2. 3R
3. 4R
4. 5R

✅ Correct Answer: 3

In previous problem the work done by external agent is:

1. 40 J
2. -40 J
3. zero
4. +10 J

✅ Correct Answer: 1

If earth were to rotate faster than its present speed the weight of an object will:

1. increase at the equator but remain unchanged at poles
2. decrease at the equator but remain unchanged at the poles
3. remain unchanged at the equator but decrease at the poles
4. remain unchanged at the equator but increase at the poles

✅ Correct Answer: 2

If the earth stops rotating about its axis the acceleration due to gravity will remain unchanged at:

1. equator
2. latitude 45 degree
3. latitude 60 degree
4. poles

✅ Correct Answer: 1

A point mass of 10 kg is placed at the centre of earth. The weight of the point mass is:

1. zero
2. 98 N
3. 49 N
4. none of these

✅ Correct Answer: 1

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth:

1. the angular momentum of S about
2. the centre of the earth changes in direction but its magnitude remains constant
3. the total mechanical energy of S varies periodically with time
4. the linear momentum of S remains constant in the magnitude

✅ Correct Answer: 1

The escape velocity on the surface of the earth is 11.2 km/s. If mass and radius of a planet are 4 and 2 times respectively than that of earth the escape velocity from the planet will be:

1. 11.2 km/s
2. 1.112 km/s
3. 15.8 km/s
4. 22.4 km/s

✅ Correct Answer: 3

The ratio of the energy required to raise a satellite upto a height R (radius of earth) from the surface of earth to that required to put it into orbit there is:

1. 1:01
2. 8:01
3. 4:01
4. 2:03

✅ Correct Answer: 4

An artificial satellite of the earth releases a packet. If air resistance is neglected the point where the packet will hit will be:

1. ahead
2. exactly below
3. behind
4. it will never reach the earth

✅ Correct Answer: 4

A body is projected vertically from the surface of the Earth with a velocity equal to half of the escape velocity. Maximum height reached by the body is

1. 5R / 3
2. R / 3
3. 2R / 3
4. R / 3

✅ Correct Answer: 4

he radius of Earth is h. If the acceleration due to gravity reduces to 1% of its value at the surface of Earth then the altitude is

1. 25h
2. 10h
3. 9h
4. 5h

✅ Correct Answer: 3

A satellite is orbiting very close to a planet. Its time period depends only upon

1. density of the planet
2. mass of the planet
3. radius of the planet
4. mass of the satellite

✅ Correct Answer: 1

If both the mass and radius of Earth decrease by 1% the value of acceleration due to gravity will decrease by nearly

1. 1%
2. 1.50%
3. 2%
4. 2.50%

✅ Correct Answer: 1

A body weighs 700 g on the surface of the Earth. How much will it weigh on the surface of a planet whose mass is 1 / 7 and radius is half that of the Earth ?

1. 200 g wt
2. 400 g wt
3. 50 g wt
4. 300 g wt

✅ Correct Answer: 2

When the body is moving up the acceleration due to gravity will be:

1. downward
2. upward
3. sideways
4. nil

✅ Correct Answer: 1

Consider the earth to be a homogeneous sphere. Scientist A goes deep down in a mine an scientist B goes high up in a balloon. The gravitational field measured by:

1. A goes on decreasing and that by B goes on increasinG
2. B goes on decreasing and that by A goes on increasing
3. each remains unchanged
4. each goes on decreasing

✅ Correct Answer: 4

A planet has twice the density of Earth but the acceleration due to gravity on the surface is same as on the surface of Earth. Its radius in terms of the radius R of Earth is

1. R / 2
2. R / 4
3. R / 8
4. R / 64

✅ Correct Answer: 1

If the speed of a satellite moving around a planet is increased by 41.4% it will:

1. move in an orbit of greater radius
2. move in an orbit of lesser radius
3. fall into the planet
4. escape from the planet

✅ Correct Answer: 4

Two identical satellite are moving around the Earth in circular orbits at heights 3R and R respectively where R is the radius of the Earth. The ratio of their kinetic energies is

1. 2:01
2. 1:02
3. 3:01
4. 2:03

✅ Correct Answer: 2

A satellite revolving around the Earth loses some energy due to collision. What would be the effect on its velocity and distance from the centre of the Earth ?

1. Velocity increases and distance decreases
2. Both velocity and distance increase
3. Both velocity and distance decrease
4. Velocity decreases and distance increases

✅ Correct Answer: 1

If the distance between the Earth and the Sun becomes half its present value the number of days in a year would have been

1. 64.5
2. 129
3. 182.5
4. 730

✅ Correct Answer: 2

Mass remaining constant the radius of the Earth shrinks by 1% .The acceleration due to gravity on the earths surface would

1. increase by 2%
2. increase by 1%
3. decrease by 1%
4. decrease by 1 / 2%.

✅ Correct Answer: 1

A planet has radius and mass both half of those of the earth then the value of g on that planet will be:

1. 4.9 m/second square
2. 9.8 m/second square
3. 19.6 m/second square
4. 13.8 m/second square

✅ Correct Answer: 3

In case of earth:

1. field is zero both at centre and infinity
2. potential is zero but at centre and infinity
3. potential is same both at centre and infinity but not zero
4. potential is minimum at the centre

✅ Correct Answer: 1

Two of Jupiter s moons have orbit radii which differ by a factor of 2. Their periods differ by

1. 8
2. 4
3. 2.8
4. 4.2

✅ Correct Answer: 3

The energy required to shift a satellite from orbital radius r to orbital radius 2r is E. What energy will be required to shift the satellite from orbital radius 2r to orbital radius 3r ?

1. E
2. E/2
3. E/3
4. E/4

✅ Correct Answer: 3

Given : R = radius of Earth. What is the approximate distance of a geostationary satellite from the centre of Earth ? [Note that the satellite is above the equator.]

1. 5R
2. 6R
3. 7R
4. 8R

✅ Correct Answer: 3

Keplers II law is a consequence of:

1. conservation of energy
2. conservation of linear momentum
3. conservation of angular momentum
4. none of the above

✅ Correct Answer: 3

Orbital velocity of satellite revolving in a circular path close to the planet

1. is directly proportional to the density of planet
2. is directly proportional to the square root of density of planet
3. is directly proportional to square of density of planet
4. is inversely proportional to square root of density of planet

✅ Correct Answer: 2

If radius of Earth is 4000 miles then the linear velocity of a body at the equator is nearly.

1. 1000 mile / h
2. 2000 mile / h
3. 3000 mile / h
4. 4000 mile / h

✅ Correct Answer: 1

The distance of two satellites P and Q from Earth are in the ratio 3 : 1. The ratio of their total energy will be

1. 3:01
2. 1:03
3. 1:01
4. 1 / 3 : 1

✅ Correct Answer: 2

If the mass of a planet is 10% less than that of the Earth and the radius 20% greater than that of the Earth the acceleration due to gravity on the planet will be

1. 5 / 8 times that on the surface of the Earth
2. 3 / 4 times that on the surface of the Earth
3. 1 / 2 times that on the surface of the Earth
4. 9 / 10 times that on the surface of the Earth

✅ Correct Answer: 1

The radius of the earth shrinks by 1%. The acceleration due to gravity on the earths surface would: (mass remaining constant)

1. increase by 2%
2. increase by 1%
3. decrease by 1%
4. decrease by 0.5%

✅ Correct Answer: 0

The time period of a satellite in a circular orbit of radius R is T. The radius of the orbit in which time period is 8T is

1. 2R
2. 3R
3. 4R
4. 5R

✅ Correct Answer: 3

Inside a uniform spherical shell:

1. potential is zero
2. field is zero
3. potential is constant
4. both B and C

✅ Correct Answer: 4

A body weighing 20 kg on the surface of the earth is taken to a place 6000 km below the earths surface. Assuming the earths radius to be 6000 km the weight of the body at that depth is:

1. 40 kg
2. 5 kg
3. infinite
4. zero

✅ Correct Answer: 4

The binding energy of a system comprising of Earth and satellite is (Letters have usual meanings)

1. GMm / r
2. GMm / 2r
3. GMm / r
4. GMm / 2r

✅ Correct Answer: 4