Question

The acceleration due to gravity on the moon is one sixth that on the earth. A high jumper can jump 2cm on earth. What distance can he jump on the moon?

A) 2m

B) 6m

C) 12m 

D) 18m

Answer 1

Hint: We have given the acceleration due to gravity on the moon in terms of earth’s acceleration due to gravity and asked distance upto which a man can jump on moon surface. When a man jumps the energy is stored in form of potential energy and we are talking about same jumper therefore the P.E. would be same irrespective of the surface. 

Formula used:   \[P.E.=mgh\]

Complete answer:

Acceleration due to gravity as the name suggest is the acceleration an object achieve due to the gravitational force. It is given that moon’s acceleration due to gravity is one sixth that on the earth. If earth’s acceleration due to gravity on earth is g and acceleration due to gravity on moon is \[{{g}_{m}}\], then given data

\[{{g}_{m}}=\dfrac{g}{6}\]

Now the potential energy is given as

\[P.E.=mgh\]

The potential energy is the energy stored in an object at a particular height relative to some zero point. Here we are taking earth’s surface as zero point and calculating height respective to the ground which will give gravitational potential energy. The potential energy will be same if the same man is considered as mass will be same irrespective on the surface the man is jumping. Hence, we can write

\[mgh=m{{g}_{m}}{{h}_{m}}\]

Where m is the mass of the jumper and h is the distance upto which the man can jump on earth surface and  \[{{h}_{m}}\] is the distance jumper can jump on the moon. 

Substituting \[{{g}_{m}}=\dfrac{g}{6}\]in the above equation, we get

$mgh=m\left( \dfrac{g}{6} \right){{h}_{m}}$

$mgh=\dfrac{mg{{h}_{m}}}{6}$

$h=\dfrac{{{h}_{m}}}{6}$

${{h}_{m}}=6h$

It is given \[h=2m\], substituting it in the above equation we get \[{{h}_{m}}=12m\].

Hence the jumper can jump up to 12m on the moon.

So, the correct answer is “Option C”.

Note: The acceleration due to gravity also varies on the earth’s surface. The acceleration due to gravity at the pole of the earth is greater than at the equator. At the center of the earth the gravitational acceleration is zero, as the net downward pull is zero. The moon’s gravity is less than earth as its mass is less as surface gravity of a body is proportional to the mass of the body.