The acceleration due to gravity on the Moon is gM. Suppose an astronaut on the Moon drops an object from a height of H. The time it would take the object to reach the Moon’s surface would be TM. The same object is dropped from the same height on Earth, where the acceleration due to gravity is gE. The time it takes the object to reach the Earth’s surface is TE. Which of the following is a correct mathematical relationship for the two times? TE=gEgM−−−√TM

TE=gEgMTM
A

TE=gMgE−−−√TM

TE=gMgETM
B

TE=gEgMTM

TE=gEgMTM
C

TE=gMgETM

TE=gMgETM
D

TE=TM

The relationship between the two times is

The given parameters:

the acceleration due to gravity on the Moon = gM

height from which the object was dropped on moon, =  H

time taken for the object to reach the moon surface, = TM

height from which the object was dropped on Earth, =  H

the acceleration due to gravity on the Earth = gE

time taken for the object to reach the Earth's surface = TE

To find:

Apply the following kinematic equation:

Height equation for the object on the moon:

Height equation for the object on the Earth:

Since the two heights are equal, set the two equation to be equal to each other to determine the relationship between the two times:

Thus, the relationship between the two times is

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