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Chapter 5: Q32. (page 133)

A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

Short Answer

Expert verified

The acceleration due to gravity near the planet鈥檚 surface is gp=2.45m/s2.

Step by step solution

01

Step 1. Given Data

The radius of the planet is rp=2re.

The radius of the Earth is re.

02

Step 2. Understanding the gravitational acceleration

In this problem, the relation of acceleration due to gravity at any location on the planet鈥檚 surface will be utilized.

03

Step 3. Calculation of the gravitational acceleration near the surface of the planet

The relation of gravitational acceleration is given by,

gp=Gmprp2

Here, mpis the mass of the planet equal to the mass of the Earth and G is the gravitational constant.

On plugging the values in the above relation.

gp=Gme2re2gp=14Gmere2gp=14ge

Here, geis the gravitational acceleration of the Earth.

Substitute the values in the above equation.

gp=149.80m/s2gp=2.45m/s2

Thus, gp=2.45m/s2is the required acceleration due to gravity.

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