Acceleration due to gravity or gravitational acceleration (g) is equal to the product of universal gravitational constant (G) and the mass (M) divided by the square of radius (r). Using the equation of gravitational acceleration: g = G M/r2, the value of gravitational acceleration on the surface of an object can be calculated.
The value of gravitational acceleration on the surface of the earth is g = 9.81 m/s2.
Let’s solve some problems based on this equation, so you’ll get a clear idea.
Gravity Practice Problems
Problem 1: Calculate the value of gravitational acceleration on the surface of the earth, if the mass of the earth is 5.972 × 1024 kg and the radius of the earth is 6.378 × 103 km. (Take the value of universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2)
Solution:
Given data:
Gravitational acceleration on the surface of the earth, g = ?
Mass of the earth, M = 5.972 × 1024 kg
Radius of the earth, r = 6.378 × 103 km = 6.378 × 106 m
Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Using the equation of gravitational acceleration,
g = G M/r2
g = (6.67 × 10-11 × 5.972 × 1024)/(6.378 × 106)2
g = (39.9 × 1013)/(40.7 × 1012)
g = 0.9803 × 10
g = 9.81 m/s2
Therefore, the gravitational acceleration on the surface of the earth is 9.81 m/s2.
Problem 2: If the mass of the jupiter is 1.898 × 1027 kg and the radius of the jupiter is 69.911 × 103 km, then calculate the value of gravitational acceleration on the surface of the jupiter. (Take the value of universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2)
Solution:
Given data:
Mass of the jupiter, M = 1.898 × 1027 kg
Radius of the jupiter, r = 69.911 × 103 km = 69.911 × 106 m
Gravitational acceleration on the surface of the jupiter, g = ?
Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Using the equation of gravitational acceleration,
g = G M/r2
g = (6.67 × 10-11 × 1.898 × 1027)/(69.911 × 106)2
g = (12.7 × 1016)/(4887.6 × 1012)
g = 0.002598 × 104
g = 25.98 m/s2
Therefore, the gravitational acceleration on the surface of the jupiter is 25.98 m/s2.
Problem 3: What is the value of gravitational acceleration on the surface of the mars, if the mass of the mars is 6.39 × 1023 kg and the radius of the mars is 3.3895 × 103 km? (Take the value of universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2)
Solution:
Given data:
Gravitational acceleration on the surface of the mars, g = ?
Mass of the mars, M = 6.39 × 1023 kg
Radius of the mars, r = 3.3895 × 103 km = 3.3895 × 106 m
Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Using the equation of gravitational acceleration,
g = G M/r2
g = (6.67 × 10-11 × 6.39 × 1023)/(3.3895 × 106)2
g = (42.7 × 1012)/(11.5 × 1012)
g = 3.71 m/s2
Therefore, the gravitational acceleration on the surface of the mars is 3.71 m/s2.
Problem 4: The mass of the moon is 7.342 × 1022 kg and the radius of the moon is 1.7371 × 103 km. Calculate the value of gravitational acceleration on the surface of the moon. (Take the value of universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2)
Solution:
Given data:
Mass of the moon, M = 7.342 × 1022 kg
Radius of the moon, r = 1.7371 × 103 km = 1.7371 × 106 m
Gravitational acceleration on the surface of the moon, g = ?
Universal gravitational constant, G = 6.67 × 10-11 Nm2/kg2
Using the equation of gravitational acceleration,
g = G M/r2
g = (6.67 × 10-11 × 7.342 × 1022)/(1.7371 × 106)2
g = (48.9 × 1011)/(3 × 1012)
g = 16.3 × 10-1
g = 1.63 m/s2
Therefore, the gravitational acceleration on the surface of the moon is 1.63 m/s2.
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