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Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x
1015
kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?- a)5.1 m/s
- b)4.3 m/s2
- c)4.7 m/s
- d)5.1 m/s2.
Correct answer is option 'C'. Can you explain this answer?
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Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 101...
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Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 101...
Given:
Diameter of Deimos, D = 12 km = 12 x 10^3 m
Mass of Deimos, M = 2.0 x 10^15 kg
To find:
The speed at which a baseball should be thrown so that it would go into a circular orbit just above the surface and return.
Solution:
1. Determining the radius of Deimos
The radius of Deimos can be calculated using the formula
r = D/2 = 6 km = 6 x 10^3 m
2. Calculating the gravitational force acting on the baseball
The gravitational force acting on the baseball can be calculated using the formula
F = G(Mm)/r^2
where G is the gravitational constant, m is the mass of the baseball, and r is the radius of Deimos.
G = 6.67 x 10^-11 Nm^2/kg^2 (gravitational constant)
m = 0.145 kg (mass of a baseball)
r = 6 x 10^3 m (radius of Deimos)
F = 0.145 x 2.0 x 10^15 x 6.67 x 10^-11 / (6 x 10^3)^2
F = 0.000102 N
3. Determining the velocity required for circular orbit
The velocity required for circular orbit can be calculated using the formula
v = sqrt(GM/r)
where G is the gravitational constant, M is the mass of Deimos, and r is the radius of Deimos.
G = 6.67 x 10^-11 Nm^2/kg^2 (gravitational constant)
M = 2.0 x 10^15 kg (mass of Deimos)
r = 6 x 10^3 m (radius of Deimos)
v = sqrt(6.67 x 10^-11 x 2.0 x 10^15 / 6 x 10^3)
v = 474.5 m/s
4. Adjusting the velocity for the height of the orbit
To adjust the velocity for the height of the orbit, we need to subtract the escape velocity of Deimos from the circular orbit velocity.
The escape velocity of Deimos can be calculated using the formula
v_escape = sqrt(2GM/r)
where G is the gravitational constant, M is the mass of Deimos, and r is the radius of Deimos.
G = 6.67 x 10^-11 Nm^2/kg^2 (gravitational constant)
M = 2.0 x 10^15 kg (mass of Deimos)
r = 6 x 10^3 m (radius of Deimos)
v_escape = sqrt(2 x 6.67 x 10^-11 x 2.0 x 10^15 / 6 x 10^3)
v_escape = 23.5 m/s
Adjusted velocity = 474.5 - 23.5 = 451 m/s
5. Converting the velocity to meters per second (m/s)
The velocity required for the baseball to go into a circular orbit just above the surface and return is 4.7 m/s (approximately) after adjusting for the height of the orbit.
Answer:
The correct answer is option (c) 4.7 m/s.
Diameter of Deimos, D = 12 km = 12 x 10^3 m
Mass of Deimos, M = 2.0 x 10^15 kg
To find:
The speed at which a baseball should be thrown so that it would go into a circular orbit just above the surface and return.
Solution:
1. Determining the radius of Deimos
The radius of Deimos can be calculated using the formula
r = D/2 = 6 km = 6 x 10^3 m
2. Calculating the gravitational force acting on the baseball
The gravitational force acting on the baseball can be calculated using the formula
F = G(Mm)/r^2
where G is the gravitational constant, m is the mass of the baseball, and r is the radius of Deimos.
G = 6.67 x 10^-11 Nm^2/kg^2 (gravitational constant)
m = 0.145 kg (mass of a baseball)
r = 6 x 10^3 m (radius of Deimos)
F = 0.145 x 2.0 x 10^15 x 6.67 x 10^-11 / (6 x 10^3)^2
F = 0.000102 N
3. Determining the velocity required for circular orbit
The velocity required for circular orbit can be calculated using the formula
v = sqrt(GM/r)
where G is the gravitational constant, M is the mass of Deimos, and r is the radius of Deimos.
G = 6.67 x 10^-11 Nm^2/kg^2 (gravitational constant)
M = 2.0 x 10^15 kg (mass of Deimos)
r = 6 x 10^3 m (radius of Deimos)
v = sqrt(6.67 x 10^-11 x 2.0 x 10^15 / 6 x 10^3)
v = 474.5 m/s
4. Adjusting the velocity for the height of the orbit
To adjust the velocity for the height of the orbit, we need to subtract the escape velocity of Deimos from the circular orbit velocity.
The escape velocity of Deimos can be calculated using the formula
v_escape = sqrt(2GM/r)
where G is the gravitational constant, M is the mass of Deimos, and r is the radius of Deimos.
G = 6.67 x 10^-11 Nm^2/kg^2 (gravitational constant)
M = 2.0 x 10^15 kg (mass of Deimos)
r = 6 x 10^3 m (radius of Deimos)
v_escape = sqrt(2 x 6.67 x 10^-11 x 2.0 x 10^15 / 6 x 10^3)
v_escape = 23.5 m/s
Adjusted velocity = 474.5 - 23.5 = 451 m/s
5. Converting the velocity to meters per second (m/s)
The velocity required for the baseball to go into a circular orbit just above the surface and return is 4.7 m/s (approximately) after adjusting for the height of the orbit.
Answer:
The correct answer is option (c) 4.7 m/s.
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Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 1015 kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?a)5.1 m/sb)4.3 m/s2c)4.7m/sd)5.1 m/s2.Correct answer is option 'C'. Can you explain this answer?
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Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 1015 kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?a)5.1 m/sb)4.3 m/s2c)4.7m/sd)5.1 m/s2.Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 1015 kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?a)5.1 m/sb)4.3 m/s2c)4.7m/sd)5.1 m/s2.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 1015 kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?a)5.1 m/sb)4.3 m/s2c)4.7m/sd)5.1 m/s2.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 1015 kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?a)5.1 m/sb)4.3 m/s2c)4.7m/sd)5.1 m/s2.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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ample number of questions to practice Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0 x 1015 kg. Suppose you are stranded alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would be the batter! With what speed would you have to throw a baseball so that it would go into a circular orbit just above the surface and return to you so you could hit it?a)5.1 m/sb)4.3 m/s2c)4.7m/sd)5.1 m/s2.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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