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WorksheetsPre-U Gravitational Fields
Total questions: 48
Worksheet time: 48mins
The Earth may be assumed to be spherical with radius r and density ⍴.
Which equation correctly relates the gravitational field strength g at its surface to these quantities and the gravitational constant G?
The gravitational field strength outside a uniform sphere of mass M is the same as that of a point mass M at the centre of the sphere. The Earth, which may be assumed to be spherical and of radius r, has a gravitational field strength g at its surface.
Which expression gives the gravitational field strength at height h above the ground?
Two isolated masses m₁ and m₂ are separated by a distance r.
Which expression gives the gravitational field strength caused by m₁ at m₂?
What is numerically equal to the gravitational field strength at a point P on the Earth's surface?
the acceleration of free fall at P
the change in potential energy per unit distance from P
the force acting on any body placed at P
the work done in bringing unit mass from infinity to P
Which statement about a uniform gravitational field is true?
Its magnitude is the same in all directions
The gravitational potential has the same value at all points within it
Its direction is opposite to the direction of motion of a test mass released in it
Its field strength is the same at all points within it
A body of mass 20 kg mass is placed 4 m above the Earth's surface. The value of g may be taken as 10 ms-2.
What are the gravitational field strength and gravitational force acting on the body?
A
B
C
D
The acceleration of free fall on the Earth's surface may be taken to be 6 times the value on the Moon's surface. The mean density of the Earth may be taken to be 5/3 times the value of the Moon. The radius of the Earth is r_E and that of the moon is r_M.
What is the ratio r_E / r_M
1.9
3.6
6.0
10
A mass m is released just above the surface of a planet with mass M and radius R.
Which expression gives its initial gravitational acceleration?
The Earth may be assumed to be spherical with mass M and radius R, with acceleration of free fall g at its surface. Which equation correctly shows how the universal gravitational constant G is related to these quantities?
The given diagram illustrates how the acceleration of free fall is determined by timing the fall of a steel ball photo-electrically. After release from P, the ball passes X and Y at time t_x and t_y.
Which expression gives the acceleration of free fall?
At the Earth's surface, the gravitational field strength is about 10 N kg-1.
At a point outside the Earth and a distance x from its centre, the field strength is about 5 N kg-1.
Which expression gives an approximate value for the radius of the Earth?
x / 5
x / 2√2
x / 2
x / √2
At the surface of a planet the acceleration of free fall is greater than that on Earth. If the planet has the same radius as the Earth, which of the following on the planet will be the same as that on the Earth?
the escape velocity of a spacecraft
the weight of an astronaut as measured by a spring balance
the height to which an astronaut can jump
the surface tension of a liquid
A uniform sphere of diameter d has a gravitational field strength X at its surface. A second uniform sphere has the same density but has a diameter 2d.
What is the gravitational field strength at the surface of the second sphere?
2X
4X
8X
16X
Which of the following is a SI unit of gravitational field strength?
m s-2
J kg-1
kg N-1
N m-1
The Earth may be taken to be a uniform sphere of radius r. In the expressions below, g is the acceleration of free fall and G is the gravitational constant.
Which expression gives the mean density of the Earth?
The acceleration of free fall g on the surfaces of two planets are the same. Which of the following expressions must be the same for the planets?
mass
radius
mass / radius
mass / (radius)2
A satellite experiences a gravitational force W when it is on the ground. It is placed in a circular orbit at a height R/50, where R is the radius of the Earth. What gravitational force would it experience?
1.04 W
1.02 W
0.98 W
0.96 W
Both the Sun of mass M_s and the Moon of mass M_m exerts gravitational forces on the Earth. The distance of the Sun from the Earth is r_s and the distance of the Moon from the Earth is r_m.
Which expression gives the value of (force on the Earth due to the Sun) / (force on the Earth due to the Moon) ?
When a satellite is at its launch site on the Earth's surface, it is found to have a weight W. When the satellite is placed in a circular orbit at a height h = 6R above the Earth's surface, where R is the radius of the Earth, what is the gravitational force acting on it?
W / 6
W / 7
W / 36
W / 49
Two small stationary masses M₁ and M₂ are separated by a distance d. A particle, lying on the line joining two masses, experiences no resultant gravitational force.
Which expression gives the distance of this particle from mass M₁?
The Earth may be taken to be a uniform sphere rotating about an axis through the poles. Which of the following correctly compares the weight of a body at the Equator relative to its weight at a pole?
greater, because angular velocity of the Earth is greater at the Equator than at a pole.
greater, because the weight at the Equator is given by the sum of the gravitational attraction of the Earth and the centripetal force due to the circular motion of the body.
the same, because the weight is the gravitational attraction of the Earth and for a uniform sphere, even when rotating, this is independent of the body's position on the Earth.
smaller, because the gravitational attraction of the Earth must provide both the weight and the centripetal force due to the circular motion of the body.
Star X of mass 2M and star Y of mass M are moving in circular orbits around their common centre of mass under their mutual gravitational attraction. The effects of any other bodies may be ignored.
What is the value of (force acting on X) / (force acting on Y) ?
4
2
1
1/2
The given diagram shows two stars of equal mass M moving at constant speed v in a circular orbit of radius R around their common centre of mass.
Which expression gives the resultant force on each star?
G M2 / (4 R)2
M v2 / (2 R)
zero
2 M v2 / R
Which of the following is a SI unit of the gravitational constant G?
m s-2
N m-2 kg-2
m3 kg-1 s-2
m2 kg-2
A planet of mass M and radius r is rotating so rapidly that objects at its equator only just remains on its surface. In the expressions below, G is the gravitational constant.
Which expression gives the planet's period of rotation?
2 π √(r/G)
2 π √(G/r)
2 π √(r3 / MG)
2 π √(MG / r3)
The radius of the Earth may be taken to be 5760 km. A satellite is in a circular orbit 144 km above the Earth's surface. What is the approximate value of the gravitational force on the satellite compared with that when it is at the Earth's surface?
greater by 10%
greater by 5%
less by 5%
less by 10%
A body of mass m, at a fixed point Q, produces a gravitational potential at point P, distance r from Q. This gravitational potential is equal to the external work done on unit mass in a defined movement.
Which of the following is the defined movement?
from P to Q
from Q to P
from P to infinity
from infinity to P
A satellite of mass 50 kg is initially placed at a point where the gravitational potential due to the Earth is -20 MJ kg-1. It is then moved to another point where the gravitational potential is -60 MJ kg-1.
In which direction did it move and what is its change in potential energy?
closer to the Earth and a loss of 2000 MJ of potential energy
closer to the Earth and a loss of 40 MJ of potential energy
further from the Earth and a gain of 2000 MJ of potential energy
further from the Earth and a gain of 40 MJ of potential energy
Each diagram below shows the variation of the gravitational potential energy U and the gravitational force F of a point mass with its distance r from another point mass.
Which one of the diagrams is correct?
The line XY joins the surface of the Earth to the surface of the Moon, as illustrated in the given diagram.
Which of the following graphs best shows how the gravitational potential Φ varies along the line XY?
The given diagram shows the variation of the gravitational potential energy E_p of a body with distance r from the centre of a planet.
What is represented by the gradient at any point on the curve?
the gravitational potential at the value of r
the gravitational field strength at that value of r
the force pulling the body towards the planet
the acceleration of the body towards the planet
Two points X and Y are at distances L and 2L from the centre of the Earth respectively. The gravitational potential at X may be taken as -8 kJ kg-1.
A 1 kg mass is moved from X and Y. What is the change in gravitational energy of the mass?
-4 kJ
-2 kJ
+4 kJ
+8 kJ
Two points X and Y are respectively at distances R and 2R from the centre of the Earth, where R is greater than the radius of the Earth. The gravitational potential at X is -800 kJ kg-1.
What is the work done on a 1 kg mass when it is moved from X to Y?
-400 kJ
-200 kJ
+200 kJ
+400 kJ
A body is released from rest at a point P a distance 3R from the centre of an isolated planet with radius R and mass M.
What is the speed of the body on hitting the planet?
A planet of mass 5.0 x 1024 kg may be taken to be a uniform sphere of radius 6.1 x 106 m. What is the energy needed to bring a mass of 2.0 kg from its surface to an infinite distance in outer space?
9.0 J
1.8 x 101 J
5.5 x 107 J
1.1 x 108 J
The escape speed is the speed which a body must have in order to escape to an infinite distance from the Earth. The escape speed of an oxygen molecule at the Earth's surface is 1.1 x 104 ms-1.
What is its escape speed at a height of 0.2 R above the Earth's surface, where R is the radius of the Earth?
0.5 x 104 ms-1
1.0 x 104 ms-1
1.1 x 104 ms-1
1.2 x 104 ms-1
A satellite of mass m is moving in a circular orbit of radius r around the Earth of mass M. The satellite remains at a vertical height h above the Earth's surface.
Gravitational potential is to be taken as zero at an infinite distance from the Earth.
Which expression gives the gravitational potential energy of the satellite?
mgh
-mgh
-GMm / r
-GMm / 2r
An object of mass m is projected from the surface of the Earth where the acceleration of free fall is g. The radius of the Earth may be taken as R. What speed must the object have in order to escape from the gravitational field of the Earth?
√(gR)
mgR
√(2gR)
mg / 2R
A point Q is further from the Earth's centre than a point P on the Earth's surface. A body is moved from P to Q. The gravitational potential energy of the body may be taken as zero when it is at an infinite distance from the Earth.
Which statement correctly describes the gravitational potential energy of the body at the two points?
It is positive at both points and numerically greater at Q than at P
It is positive at both points and numerically less at Q than at P
It is negative at both points and numerically less at Q than at P
It is negative at both points and numerically greater at Q than at P
A spacecraft is launched from the surface of the Earth. At height x above the Earth's surface, the change in gravitational potential energy of its hull is ΔV.
Which graph best shows how ΔV varies with x during the first few hundred metres after launch?
Which one of the following is not applicable to geostationary orbits?
A geostationary orbit must be directly above the equator
All satellites in a geostationary orbit must have the same mass
The period of a geostationary orbit must be 24 hours
There is only one possible radius for a geostationary orbit
Several satellites are in geostationary orbits around the Earth. Which of the following quantities is not necessarily the same for all the satellites?
angular velocity
centripetal acceleration
kinetic energy
orbital period
An old weather satellite orbit the Earth with a period of 24 hours.
It is replaced by a new satellite with the same orbit period of 24 hours, but with twice the mass.
What is the value of ratio (radius of orbit of new satellite) / (radius of orbit of old satellite) ?
1/2
1/1
√2 / 1
2/1
The Earth of mass M has an angular velocity of rotation ω. A satellite of mass m is moving in an orbit such that it remains vertically above a fixed point on the Earth's equator.
Which expression gives the radius of the satellite's orbit?
In one planetary system, a planet P₁ of mass M₁ orbits around a sun of mass S₁. In another planetary system, a planet P₂ of mass M₂ orbits around a sun of mass S₂. The two systems are widely separated. P₁ and P₂ have the same orbit radii but P₁ completes its orbit in half the time taken by P₂.
Which of the following could be deduced?
S₁ = S₂ and M₁ = 0.25 M₂
S₁ = 4 S₂ only
S₁ = 4 S₂ and M₁ = M₂
S₁ = 0.25 S₂ only
A planet of mass P is moving in a circular orbit of radius R around a sun of mass S. Which expression correctly shows how the orbit period T depends on P, R, S?
T ∝ P2
T ∝ R1/2
T ∝ R3/2
T ∝ S1/2
A satellite is moved from one circular orbit around the Earth to another circular orbit with a larger orbital radius. As a result of the change, which quantity of the satellite will increase?
gravitational force
gravitational potential energy
angular velocity
linear orbital speed
Which situational will allow the person concerned to experience "weightlessness"?
(Effects such as air resistance may be ignored, where necessary).
a driver equipped so that he remains at constant depth below the water surface without any effort on his part
an astronaut in a Moon-lander vehicle as it uses retro-rockets to make a soft landing on the Moon
an athlete clearing the bar in a high jump
a parachutist descending at terminal velocity with the parachute fully open
