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State
Newton’s Law of Gravitation, highlighting its limitation. Explain how the
Law can also be applied to spherical objects such as planets. |
4
marks |
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Newton's Law of Gravitation |
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Every particle of matter attracts every other
particles with a force whose magnitude is given by |
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where m1 and m2
are the masses of the particles and r is the distance between them.
G is a universal constant. |
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It can be proved that a thin uniform spherical
shell of mass attracts other external particles as if the shell's mass
were concentrated at its center. |
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A spherical body can be thought of as many
uniform thin shells grouped together. Therefore, it attracts external particles
as if a point mass at the center, i.e. Newton's Law also applies
for spherical body. |
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| b. |
What
is meant by a gravitational field? Illustrate how the radial gravitational
field of a planet could be represented graphically, stating the physical
significance of your drawing. |
3
marks |
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A gravitational field is a region in which any body
that has mass will experience a force of attraction. |
1 |
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The direction of the field lines points towards the center.
It means that if a test mass is placed in the field, it would be attracted
towards the spherical mass. |
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The separation of the lines is closer near the spherical
mass. It means that the strength of the field is higher near the mass. |
0.5 |
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| c. |
Define
gravitational field strength and discuss how it is related to the acceleration
of a test mass which is free to move in the field. |
2
marks |
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The gravitational field strength is the force
per unit mass on a test mass. Suppose a test mass mo
experiences gravitational force F, the field strength at that point
is
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Since the test mass is free to move, the net
force is the gravitational force. By Newton's 2nd Law, F = m a,
the acceleration is |
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| d. |
Given
a known mass, suggest a method to measure the gravitational field strength
on the Earth’s surface, stating how the result is affected by the Earth’s
self-rotation. |
4
marks |
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0.5 |
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Measure the weight W of the known mass by suspending
it under a spring balance. |
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The gravitational field strength is given by |
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Alternative method: Measure the acceleration
of free fall. Drop the mass from a height Measure the time taken and applies
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Since objects on Earth are rotating with the
Earth, they are performing circular motion. |
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The centripetal force is given by the difference
between the tension and the gravitational pull. |
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Thus, the field strength measured in this way
is less than the actual value. |
0.5 |
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| e. |
Suggest
three different ways in which radio communication are being carried out
nowadays. |
3
marks |
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The three commonly used methods are: |
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direct line-of-sight
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sky wave: reflection by ionosphere
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space wave: relayed by satellite
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