Concerete block of mass `m_(A) and m_(B)`. The gravitutional potential energy of each system is zero at the equilibrium position of the springs. Which ststement is true for the total machanical energy of the springs. Which system when the block , are balanced on the springs?

Options

A. `E_(A) = E_(B)`
B. `E_(A) = 2 E_(B)`
C. `E_(A) = 4 E_(B)`
D. `E_(A) = -2 E_(B)`

Answer

C

Explanation

`Kx_(A) = m_(A) g`
`Kx_(B) = m_(B) g implies (x_(A))/(x_(B)) = (m_(A))/(m_(B)) = 2 implies x_(A) = 2 x_(B)`
`PE_(A) = (1)/(2) K x_(A)^(2) PE_(B) = K x_(B)^(2) implies (PE_(A))/(PE_(B)) = ((x_(A))/(x_(B)))^(2) = 4`
So for `A`, potential energy of spring is four times that for `B`.
So `E_(A) = 4E_(B)`