State whether the following statement is true or false and state why it is so .
Thee value of 'g' on the moon is about 1/6th of the value of 'g' on Earth.

Question

State whether the following statement is true or false and state
why it is so
Thee value of 'g' on the moon is about 1/6th of the value of 'g' on
Earth

Sejal Gupta · Accepted Answer

Solution :

The statement is true

Suppose we have an
object of mass m and let its acceleration due to gravity
on the moon will be gm Again suppose that the mass of the moon is M
and its radius is R Thus, acceleration due to gravity of the object
on the moon will be,

gm=GMR2 (i)

Let us consider the acceleration due to gravity
of the same object on the earth is ge As we know that the mass of
the earth is 100 times that of the moon and the radius of the earth
is 4 times that of the moon, so the mass of the earth will be
100M and its radius will be 4R Now, the
acceleration due to gravity of the object on the earth will
be,

ge=G×100M4R2

or, ge=G×100M16R2 (ii)

Now, dividing equation (i) by (ii), we
get,

gmge=G×M×16R2R2×G×100Mor,          gmge =16100or,           gmge=16or,          gm=16 ge

Hence, it is proved that the acceleration due
to gravity of an object on the moon will be around one-sixth from
that of on the earth

State whether the following statement is true or false and state why it is so . Thee value of 'g' on the moon is about 1/6th of the value of 'g' on Earth.

State whether the following statement is true or false and state why it is so .
Thee value of 'g' on the moon is about 1/6th of the value of 'g' on Earth.