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Q. 21

Expert-verified
Found in: Page 354

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# You have been visiting a distant planet. Your measurements have determined that the planet’s mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large. a. What is the planet’s radius? b. To get back to earth, you need to escape the planet. What minimum speed does your rocket need?

a. The radius of the planet is

b. The minimum speed that the rocket needs is

See the step by step solution

## Part (a) Step 1 : Given information

The planet’s mass is twice that of the earth.

## Part (a) Step 2 : Calculation

Acceleration due to gravity is given by :

Where 'G' is the universal gravitational constant.

is the mass of the planet.

is the radius of the planet.

a is the acceleration due to gravity.

## Part (a) Step 3 : Continuation of calculation

Now calculating we get,

## Part (a) Step 4 : Final answer

The radius of the planet is

## Part (b) Step 5 : Given information

Free-fall acceleration is one-fourth of the gravity of the earth.

## Part (b) Step 6 : Calculation

The formula for escape velocity is given by :

Where 'v' is escape velocity.

Now,

## Part (b) Step 7 : Final answer

The minimum speed that the rocket needs is

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