Gravitation
Q. A body is thrown vertically upwards with a speed of 20 m/s. How high will it rise before coming to rest?
A.
20 m
B.
40 m
C.
10 m
D.
30 m
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Solution
Using the formula h = v²/(2g), where g = 10 m/s², h = (20)²/(2*10) = 20 m.
Correct Answer: B — 40 m
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Q. A body is thrown vertically upwards with a speed of 20 m/s. How high will it rise? (g = 10 m/s²)
A.
20 m
B.
40 m
C.
30 m
D.
10 m
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Solution
Using v² = u² - 2gh, 0 = (20)² - 2*10*h, h = 20 m.
Correct Answer: B — 40 m
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Q. A body is thrown vertically upwards with a velocity of 20 m/s. How high will it rise before coming to rest? (g = 10 m/s²)
A.
20 m
B.
40 m
C.
10 m
D.
30 m
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Solution
Using v² = u² - 2gh, 0 = (20)² - 2*10*h; h = 20 m.
Correct Answer: C — 10 m
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Q. A mass 'm' is lifted to a height 'h' above the Earth's surface. What is the change in gravitational potential energy?
A.
mgh
B.
mg(h + R)
C.
mgR
D.
0
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Solution
The change in gravitational potential energy when a mass m is lifted to a height h is given by ΔU = mgh.
Correct Answer: A — mgh
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Q. A mass m is lifted to a height h in a uniform gravitational field. What is the work done against gravity?
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Solution
The work done against gravity when lifting a mass m to a height h is given by W = mgh.
Correct Answer: A — mgh
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Q. A satellite is in a circular orbit around the Earth. How does the gravitational potential energy change as it moves to a higher orbit?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
As the satellite moves to a higher orbit, its gravitational potential energy increases.
Correct Answer: A — It increases.
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Q. A satellite is in a circular orbit around the Earth. If it moves to a higher orbit, what happens to its potential energy?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
As the satellite moves to a higher orbit, its gravitational potential energy increases due to the increase in distance from the Earth's center.
Correct Answer: A — It increases.
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Q. A satellite is in a circular orbit around the Earth. If its orbital radius is 4R, what is the gravitational force acting on it compared to that at the surface of the Earth?
A.
1/4
B.
1/16
C.
1/8
D.
1/2
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Solution
The gravitational force decreases with the square of the distance. At 4R, the force is 1/(4^2) = 1/16 of the force at the surface.
Correct Answer: B — 1/16
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Q. A satellite is in a circular orbit around the Earth. If its orbital radius is tripled, how does the orbital speed change?
A.
It triples
B.
It doubles
C.
It remains the same
D.
It is reduced to one-third
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Solution
Orbital speed v = √(GM/R). If R is tripled, v becomes √(GM/(3R)) = v/√3, which is reduced to one-third.
Correct Answer: D — It is reduced to one-third
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Q. A satellite is in a circular orbit around the Earth. If its speed is doubled, what happens to the radius of its orbit?
A.
It remains the same
B.
It doubles
C.
It increases by a factor of four
D.
It decreases by a factor of four
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Solution
If the speed of a satellite is doubled, the radius of its orbit decreases by a factor of four due to the relationship between speed and radius in circular motion.
Correct Answer: D — It decreases by a factor of four
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Q. A satellite is in a circular orbit around the Earth. If its speed is doubled, what will happen to its orbital radius?
A.
It will remain the same.
B.
It will double.
C.
It will increase by a factor of four.
D.
It will decrease by a factor of four.
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Solution
If the speed of a satellite is doubled, the orbital radius will decrease by a factor of four, as orbital speed is inversely proportional to the square root of the radius.
Correct Answer: D — It will decrease by a factor of four.
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Q. A satellite is in a circular orbit around the Earth. If its speed is increased, what will happen to its orbit?
A.
It will remain circular
B.
It will become elliptical
C.
It will crash into the Earth
D.
It will escape Earth's gravity
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Solution
Increasing the speed of a satellite in a circular orbit will cause its orbit to become elliptical.
Correct Answer: B — It will become elliptical
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Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is halved, what happens to the gravitational force acting on the satellite?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It decreases by half
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Solution
The gravitational force is inversely proportional to the square of the distance; halving the radius increases the force by a factor of four.
Correct Answer: C — It quadruples
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Q. A satellite is in a circular orbit around the Earth. If the satellite's speed is increased, what will happen to its orbit?
A.
It will remain circular
B.
It will become elliptical
C.
It will crash into the Earth
D.
It will escape Earth's gravity
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Solution
Increasing the speed of a satellite in a circular orbit will cause it to move into an elliptical orbit.
Correct Answer: B — It will become elliptical
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Q. A satellite is in a circular orbit around the Earth. What happens to its gravitational potential energy as it moves to a higher orbit?
A.
It increases.
B.
It decreases.
C.
It remains constant.
D.
It becomes zero.
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Solution
As the satellite moves to a higher orbit, its distance from the Earth increases, leading to an increase in gravitational potential energy.
Correct Answer: A — It increases.
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Q. A satellite is in a circular orbit around the Earth. What is the gravitational potential energy of the satellite?
A.
It is positive.
B.
It is negative.
C.
It is zero.
D.
It is constant.
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Solution
The gravitational potential energy of a satellite in orbit is negative due to the attractive force of gravity.
Correct Answer: B — It is negative.
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Q. A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed v and the radius r of the orbit?
A.
v = sqrt(G * M / r)
B.
v = G * M / r^2
C.
v = r * sqrt(G / M)
D.
v = G * r / M
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Solution
The orbital speed of a satellite is given by v = sqrt(G * M / r), where M is the mass of the Earth.
Correct Answer: A — v = sqrt(G * M / r)
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Q. A satellite is in a circular orbit around the Earth. What is the relationship between its orbital speed (v) and the radius of the orbit (r)?
A.
v = sqrt(G * M / r)
B.
v = G * M / r
C.
v = r / G * M
D.
v = G * r / M
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Solution
The orbital speed of a satellite is given by v = sqrt(G * M / r), where M is the mass of the Earth.
Correct Answer: A — v = sqrt(G * M / r)
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Q. A satellite is in a circular orbit at a height of 300 km above the Earth's surface. What is the approximate speed of the satellite?
A.
7.9 km/s
B.
5.0 km/s
C.
10.0 km/s
D.
3.5 km/s
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Solution
The orbital speed can be calculated using the formula v = √(GM/r). For a height of 300 km, the speed is approximately 7.9 km/s.
Correct Answer: A — 7.9 km/s
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Q. A satellite is in a polar orbit. What is the significance of this orbit?
A.
It allows the satellite to cover the entire surface of the Earth.
B.
It is the fastest orbit available.
C.
It is used only for communication satellites.
D.
It is the most stable orbit.
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Solution
A polar orbit allows the satellite to pass over the entire surface of the Earth as the planet rotates beneath it.
Correct Answer: A — It allows the satellite to cover the entire surface of the Earth.
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Q. A satellite orbits the Earth at a height of 500 km. What is the approximate gravitational acceleration experienced by the satellite?
A.
9.8 m/s²
B.
7.9 m/s²
C.
8.7 m/s²
D.
6.0 m/s²
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Solution
The gravitational acceleration experienced by a satellite at a height of 500 km is approximately 8.7 m/s².
Correct Answer: C — 8.7 m/s²
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Q. At what distance from a mass M does the gravitational potential become zero?
A.
At infinity
B.
At the surface of the mass
C.
At 1 meter
D.
At 2 meters
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Solution
The gravitational potential becomes zero at infinity, as V approaches zero as r approaches infinity.
Correct Answer: A — At infinity
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Q. At what point between two equal masses does the gravitational force become zero?
A.
At the midpoint
B.
At a point closer to one mass
C.
At a point closer to the other mass
D.
It never becomes zero
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Solution
The gravitational forces exerted by both masses cancel each other out at the midpoint.
Correct Answer: A — At the midpoint
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Q. At what point in a gravitational field is the gravitational potential constant?
A.
At the center of the mass
B.
At infinity
C.
Along an equipotential surface
D.
At the surface of the mass
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Solution
The gravitational potential is constant along an equipotential surface.
Correct Answer: C — Along an equipotential surface
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Q. At what point in space is the gravitational potential energy of an object zero?
A.
At the center of the Earth
B.
At infinity
C.
At the surface of the Earth
D.
At the Moon
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Solution
The gravitational potential energy is considered zero at infinity.
Correct Answer: B — At infinity
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Q. At what point in space is the gravitational potential zero?
A.
At the center of the Earth.
B.
At infinity.
C.
At the surface of the Earth.
D.
At the center of the Moon.
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Solution
The gravitational potential is considered zero at infinity.
Correct Answer: B — At infinity.
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Q. For a satellite in a circular orbit, which of the following is true about its kinetic and potential energy?
A.
K.E. = P.E.
B.
K.E. > P.E.
C.
K.E. < P.E.
D.
K.E. = 0
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Solution
For a satellite in a circular orbit, the kinetic energy is less than the potential energy, as K.E. = -1/2 P.E.
Correct Answer: C — K.E. < P.E.
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Q. For a satellite in a low Earth orbit, what is the approximate altitude range? (2000)
A.
200-2000 km
B.
500-10000 km
C.
1000-20000 km
D.
30000-40000 km
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Solution
Low Earth orbit satellites typically operate at altitudes ranging from about 200 km to 2000 km above the Earth's surface.
Correct Answer: A — 200-2000 km
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Q. For a satellite in a stable orbit, what must be true about the centripetal force and gravitational force?
A.
Centripetal force is greater than gravitational force
B.
Centripetal force is less than gravitational force
C.
Centripetal force equals gravitational force
D.
Centripetal force is independent of gravitational force
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Solution
For a satellite in a stable orbit, the centripetal force required for circular motion equals the gravitational force acting on the satellite.
Correct Answer: C — Centripetal force equals gravitational force
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Q. How does the gravitational field strength vary with distance from a point mass?
A.
It increases linearly.
B.
It decreases with the square of the distance.
C.
It remains constant.
D.
It decreases linearly.
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Solution
The gravitational field strength decreases with the square of the distance from the point mass.
Correct Answer: B — It decreases with the square of the distance.
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