The acceleration due to gravity on the surface of earth is 10 m/s". The average density of the planet is twice that the average density of earth and radius of a planet is half that of radius of earth. An astronaut weighing 50 kg on earth goes to this planet in a spaceship with constant velocity. Find weight of the astronaut (in Newton) on the surface of this planet.
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Answer:
Hey Friend!
Here's your answer :
Given:
- Acceleration due to gravity on Earth, g = 10 m/s^2
- Average density of the planet, rho_p = 2 * rho_e (where rho_e is the average density of Earth)
- Radius of the planet, R_p = 0.5 * R_e (where R_e is the radius of Earth)
- Weight of the astronaut on Earth, W_e = 50 kg
We need to find the weight of the astronaut on the surface of the planet in Newtons.
The formula for the acceleration due to gravity on a planet is:
g_p = (G * M_p) / R_p^2
where G is the gravitational constant, M_p is the mass of the planet, and R_p is the radius of the planet.
The mass of the planet can be calculated using the formula:
M_p = (4/3) * pi * R_p^3 * rho_p
Substituting the given values in the above formulas, we get:
R_p = 0.5 * R_e = 0.5 * 6400 km = 3200 km = 3.2 * 10^6 m
rho_p = 2 * rho_e
M_p = (4/3) * pi * R_p^3 * rho_p
= (4/3) * pi * (3.2 * 10^6)^3 * 2 * rho_e
= 1.024 * 10^23 kg
g_p = (G * M_p) / R_p^2
= (6.67 * 10^-11) * (1.024 * 10^23) / (3.2 * 10^6)^2
= 40 m/s^2
The weight of the astronaut on the surface of the planet can be calculated using the formula:
W_p = m * g_p
Substituting the given values, we get:
W_p = 50 kg * 40 m/s^2
= 2000 N
Therefore, the weight of the astronaut on the surface of this planet is 2000 Newtons.
Hope that helped you!
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-A r i a
Answer:
The acceleration due to gravity on the surface of earth is 10 m/s". The average density of the planet is twice that the average density of earth and radius of a planet is half that of radius of earth. An astronaut weighing 50 kg on earth goes to this planet in a spaceship with constant velocity. Find weight of the astronaut (in Newton) on the surface of this planet.
Explanation:
The acceleration due to gravity on the surface of earth is 10 m/s". The average density of the planet is twice that the average density of earth and radius of a planet is half that of radius of earth. An astronaut weighing 50 kg on earth goes to this planet in a spaceship with constant velocity. Find weight of the astronaut (in Newton) on the surface of this planet.
The acceleration due to gravity on the surface of earth is 10 m/s". The average density of the planet is twice that the average density of earth and radius of a planet is half that of radius of earth. An astronaut weighing 50 kg on earth goes to this planet in a spaceship with constant velocity. Find weight of the astronaut (in Newton) on the surface of this planet.
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