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/r**** ^{2}**, 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/s**** ^{2}**.

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 × 10^{24} kg and the radius of the earth is 6.378 × 10^{3} km. (Take the value of universal gravitational constant, G = 6.67 × 10^{-11} Nm^{2}/kg^{2})

Solution:

Given data:

Gravitational acceleration on the surface of the earth, g = ?

Mass of the earth, M = 5.972 × 10^{24} kg

Radius of the earth, r = 6.378 × 10^{3} km = 6.378 × 10^{6} m

Universal gravitational constant, G = 6.67 × 10^{-11} Nm^{2}/kg^{2}

Using the equation of gravitational acceleration,

g = G M/r^{2}

g = (6.67 × 10^{-11} × 5.972 × 10^{24})/(6.378 × 10^{6})^{2}

g = (39.9 × 10^{13})/(40.7 × 10^{12})

g = 0.9803 × 10

g = 9.81 m/s^{2}

Therefore, the gravitational acceleration on the surface of the earth is **9.81 m/s ^{2}**.

**Problem 2:** If the mass of the jupiter is 1.898 × 10^{27} kg and the radius of the jupiter is 69.911 × 10^{3} 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} Nm^{2}/kg^{2})

Solution:

Given data:

Mass of the jupiter, M = 1.898 × 10^{27} kg

Radius of the jupiter, r = 69.911 × 10^{3} km = 69.911 × 10^{6} m

Gravitational acceleration on the surface of the jupiter, g = ?

Universal gravitational constant, G = 6.67 × 10^{-11} Nm^{2}/kg^{2}

Using the equation of gravitational acceleration,

g = G M/r^{2}

g = (6.67 × 10^{-11} × 1.898 × 10^{27})/(69.911 × 10^{6})^{2}

g = (12.7 × 10^{16})/(4887.6 × 10^{12})

g = 0.002598 × 10^{4}

g = 25.98 m/s^{2}

Therefore, the gravitational acceleration on the surface of the jupiter is **25.98 m/s ^{2}**.

**Problem 3:** What is the value of gravitational acceleration on the surface of the mars, if the mass of the mars is 6.39 × 10^{23} kg and the radius of the mars is 3.3895 × 10^{3} km? (Take the value of universal gravitational constant, G = 6.67 × 10^{-11} Nm^{2}/kg^{2})

Solution:

Given data:

Gravitational acceleration on the surface of the mars, g = ?

Mass of the mars, M = 6.39 × 10^{23} kg

Radius of the mars, r = 3.3895 × 10^{3} km = 3.3895 × 10^{6} m

Universal gravitational constant, G = 6.67 × 10^{-11} Nm^{2}/kg^{2}

Using the equation of gravitational acceleration,

g = G M/r^{2}

g = (6.67 × 10^{-11} × 6.39 × 10^{23})/(3.3895 × 10^{6})^{2}

g = (42.7 × 10^{12})/(11.5 × 10^{12})

g = 3.71 m/s^{2}

Therefore, the gravitational acceleration on the surface of the mars is **3.71 m/s ^{2}**.

**Problem 4:** The mass of the moon is 7.342 × 10^{22} kg and the radius of the moon is 1.7371 × 10^{3} 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} Nm^{2}/kg^{2})

Solution:

Given data:

Mass of the moon, M = 7.342 × 10^{22} kg

Radius of the moon, r = 1.7371 × 10^{3} km = 1.7371 × 10^{6} m

Gravitational acceleration on the surface of the moon, g = ?

Universal gravitational constant, G = 6.67 × 10^{-11} Nm^{2}/kg^{2}

Using the equation of gravitational acceleration,

g = G M/r^{2}

g = (6.67 × 10^{-11} × 7.342 × 10^{22})/(1.7371 × 10^{6})^{2}

g = (48.9 × 10^{11})/(3 × 10^{12})

g = 16.3 × 10^{-1}

g = 1.63 m/s^{2}

Therefore, the gravitational acceleration on the surface of the moon is **1.63 m/s ^{2}**.

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