Arobotic rover on mars finds a spherical rock with a diameter of 10 centimeters [cm]. the rover picks up the rock and lifts it 20 centimeters [cm] straight up. the resulting potential energy of the rock relative to the surface is 2 joules [j]. gravitational acceleration on mars is 3.7 meters per second squared [m/s2]. what is the specific gravity of the rock?

5166.347

Explanation:

The specific gravity of a solid (also called relative density) is the ratio of the density of that solid to the density of water (normally at ):

(1)

On the other hand, the density of the rock is calculated by:

(2)

Where:

is the mass of the rock

is the volume of the rock, since is spherical

Well, we already know the value of , but we need to find in order to find the rock's specific gravity; and in order to do this, we firsly have to find and then calculate :

In the case of the mass of the rock, we can calclate it by the following equation:

(3)

Where:

is the weight if the rock in mars

is the acceleration due gravity in Mars

Isolating :

(4)

(5)

To find we can use the following equation of the potential gravitational energy :

(6)

Where:

is the potential energy

is the height at which the rock has the mentioned potential energy

Isolating :

(7)

(8)

(9)

Substituting (9) in (5):

(10)

(11)

Substituting (11) in (2):

(12) At this point we only need to find the volume of the rock, knowing its diameter is , hence its radius is

(13)

(14)

Substituting (14) in (12):

(15)

(16)

Substituting (16) in (1):

(17)

Finally we obtain the specific gravity of the rock:

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