# NCERT Class 11 Physics Solutions: Chapter 8 – Gravitation-Part 9

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**Question 8.24:**

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship; mass of the Sun ; mass of mars kg; radius of mars ; radius of the orbit of mars G

**Answer:**

Mass of the spaceship

Mass of the Sun,

Mass of Mars,

Orbital radius of Mars,

Radius of Mars,

Universal gravitational constant,

Potential energy of the spaceship due to the gravitational attraction of the Sun,

Potential energy of the spaceship due to the gravitational attraction of Mars

Since the spaceship is stationed on Mars, its velocity and hence, its kinetic energy will be zero.

Total energy of the spaceship

The negative sign indicates that the system is in bound state.

Energy required for launching the spaceship out of the solar system Total energy of the spaceship

**Question 8.25:**

A rocket is fired ‘vertically’ from the surface of mars with a speed of If of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars ; radius of mars ;

**Answer:**

Initial velocity of the rocket,

Mass of Mars,

Radius of Mars,

Universal gravitational constant,

Mass of the rocket

Initial kinetic energy of the rocket

Initial potential energy of the rocket

Total initial energy

If of initial kinetic energy is lost due to Martian atmospheric resistance, then only of its kinetic energy helps in reaching a height.

Total initial energy available

Maximum height reached by the rocket

At this height, the velocity and hence, the kinetic energy of the rocket will become zero.

Total energy of the rocket at height

Applying the law of conservation of energy for the rocket, we can write: