A ball has [tex][tex]$116.62 J$[/tex][/tex] of gravitational potential energy at a height of [tex][tex]$85 m$[/tex][/tex]. What is the mass of the ball?

A. [tex][tex]$0.14 kg$[/tex][/tex]
B. [tex][tex]$0.37 kg$[/tex][/tex]
C. [tex][tex]$11.9 kg$[/tex][/tex]



Answer :

To determine the mass of a ball using its gravitational potential energy, we can use the formula for gravitational potential energy, which is given by:

[tex]\[ PE = m \cdot g \cdot h \][/tex]

Where:
- [tex]\( PE \)[/tex] is the gravitational potential energy, in Joules (J).
- [tex]\( m \)[/tex] is the mass, in kilograms (kg).
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.81 \, m/s^2 \)[/tex].
- [tex]\( h \)[/tex] is the height above the ground, in meters (m).

Given values:
- [tex]\( PE = 116.62 \, J \)[/tex]
- [tex]\( h = 85 \, m \)[/tex]
- [tex]\( g = 9.81 \, m/s^2 \)[/tex]

We need to solve for the mass ([tex]\( m \)[/tex]). Rearrange the formula to solve for [tex]\( m \)[/tex]:

[tex]\[ m = \frac{PE}{g \cdot h} \][/tex]

Substitute the given values into this equation:

[tex]\[ m = \frac{116.62 \, J}{9.81 \, m/s^2 \cdot 85 \, m} \][/tex]

Perform the calculation:

[tex]\[ m \approx 0.1398572884811417 \, kg \][/tex]

Rounding to two decimal places, the mass [tex]\( m \)[/tex] is approximately [tex]\( 0.14 \, kg \)[/tex].

So, the mass of the ball is:

[tex]\[ 0.14 \, kg \][/tex]

This matches the first option:

[tex]\[ \boxed{0.14 \, kg} \][/tex]