Answer:
The 10 kg mass would have to be at a height 3 times that of the 30 kg mass to have the same gravitational potential energy as the 30 kg mass.
Explanation:
Gravitational potential energy, U = mgh where m = mass of object, g = acceleration due to gravity = 9.8 m/s² and h = height of object above the ground.
Now, let U' = gravitational potential energy of 10 kg mass = m'gh' where m' = 10 kg and h' = height of 10 kg mass above the ground.
So, U' = 10gh'
Also, let U" = gravitational potential energy of 30 kg mass = m"gh" where m" = 30 kg and h" = height of 30 kg mass above the ground.
So, U" = 30gh"
Since both object are supposed to have the same potential energy at a given height of the 10 kg mass,
U' = U"
10gh' = 30gh"
h' = 30gh"/10g
h' = 3h"
So, the 10 kg mass would have to be at a height 3 times that of the 30 kg mass to have the same gravitational potential energy as the 30 kg mass.
