Question

A man covers a 60-meter distance in one minute on the surface of the earth. The distance he will cover on the surface of the moon per minute is:
 (assuming ${g_{moon}} = \dfrac{{{g_{earth}}}}{6}$)
(A) $60m$
(B) $60 \times 6m$
(C) $\dfrac{{60}}{6}m$
(D) $\sqrt {60} m$

Answer 1

Hint: The man is moving on the surface tangentially and the acceleration due to gravity is acting perpendicular to the motion i.e. vertically.

Complete step by step answer:
-In this question a man is traveling 60-meter distance in one minute on the surface of the earth then what distance will recover permanently on the moon surface. Before solving we must understand what the differences between the surface of the earth and the surface of the moon are.
-The gravitational field of the earth is 6 times the gravitational field of the moon, this means that the acceleration due to gravity on earth surface will be 6 times the acceleration due to gravity on the moon surface .due to this fact the weight of an object which is measured on earth surface will be 6 times the weight of the same object if measured on the moon surface.
-Here a person is covering 60-meter distance per minute on the earth’s surface, which means he has a velocity of 60 meters per second, but this velocity is along the surface of the earth. So, it is not affected by the acceleration due to gravity of the earth because that is perpendicular to the surface.
-Since the velocity of the person does not depend upon the acceleration due to gravity of a planet, he will have the same velocity on any other planet’s surface i.e. even on the surface of the moon. Therefore, the distance he will cover on the moon surface in one minute will also be 60 meters.
Hence, option (A) is the correct one.

Note:Although ideally we are assuming that if we move with the velocity along the surface of the earth, it will be same on any other planet surface but it isn't true because when we move on the earth’s surface, we move forward because of the reaction force of the earth that we apply on it in backward direction. This means we move forward because of the contact force of the surface and contact force depends on the acceleration due to gravity of the planet. Therefore, there would be a difference in speeds on different planet surfaces.