Question

Assertion:
The escape velocity from the surface of Jupiter is found to be less than that from the earth's surface.
Reason: The radius of Jupiter is smaller than that of earth.
A. both the assertion and reason are correct and the reason is given as the correct explanation of the assertion.
B. both the assertion and reason are correct but the reason is not given as the correct explanation of the assertion.
C. assertion is correct but the reason is incorrect.
D. both assertion and reason are incorrect.

Answer 1

Hint: The escape velocity of a body is the minimum velocity required to escape from the gravitational attraction in any surfaces into the space. It is found by taking the square root of the twice the acceleration due to gravity and the radius of the surface. Jupiter is found to be the biggest planet in the solar system. The escape velocity is related with the radius of the planet. Hope these all may help you to get into the answer.

Complete answer:
The escape velocity on the earth surface is given by the equation,
\[v=\sqrt{\dfrac{GM}{R}}\]
Where $g$ be the acceleration due to gravity on the surface of earth and $R$ be the radius of earth.
As we all know that the radius of Jupiter is found to be $11$ times greater than that of the earth. There is a difference in the acceleration due to gravity also. The acceleration due to gravity on the Jupiter surface is $2.36$ times the acceleration due to gravity of the earth surface. Therefore, the escape velocity from Jupiter is surely higher than that from the surface of earth. Therefore both the assertion and reason are incorrect and the reason is not the explanation of the assertion.

So, the correct answer is “Option D”.

Note:
The existence of escape velocity is the result of conservation of energy. For a body with a certain total energy, which is moving according to conservative forces like the gravitational force, the object can reach only the combinations of locations and speeds which have that total energy. And the places which are having a higher potential energy than this will not be reached.