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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# Assume that the core of the Sun has one-eighth of the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius. Assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun’s energy is generated there. If the Sun continues to burn hydrogen at the current rate of ${\mathbf{6}}{\mathbf{.}}{\mathbf{2}}{\mathbf{×}}{{\mathbf{10}}}^{{\mathbf{11}}}{\mathbf{}}{\mathbit{k}}{\mathbit{g}}{\mathbf{/}}{\mathbit{s}}$, how long will it be before the hydrogen is entirely consumed? The Sun’s mass is ${\mathbf{2}}{\mathbf{.}}{\mathbf{0}}{\mathbf{×}}{{\mathbf{10}}}^{{\mathbf{30}}}{\mathbf{}}{\mathbit{k}}{\mathbit{g}}$.

The required time is $5×{10}^{9}years$.

See the step by step solution

## Step 1: Describe the expression for the time needed for hydrogen to burn

The expression for the time needed for hydrogen to burn is given by,

## Step 2: Find the need for hydrogen to burn

Substitute all the known values in equation (1).

Therefore, the required time is $5×{10}^{9}years$.