Question

For a particle performing SHM when displacement is x, the potential energy and restoring force acting on it is denoted by E and F, respectively. The relation between x, E and F is ____________.

Options

• `"E"/"F" + "x" = 0`

• `(2"E")/"F" + "x" = 0`

• `(2"E")/"F" - "x" = 0`

• `"E"/"F" - "x" = 0`

Answer 1

For a particle performing SHM when displacement is x, the potential energy and restoring force acting on it is denoted by E and F, respectively. The relation between x, E and F is `underline((2"E")/"F" + "x" = 0)`.

Explanation:

The restoring force acting on the particle in SHM,

F = −kx ...............(i)

The potential energy in SHM, E = `1/2 "kx"^2` ....(ii)

From Eqs. (i) and (ii), we get

E = `1/2 xx ((-"F")/"x") xx "x"^2 = -("Fx")/2`

or `(2"E")/"F"` = −x or `(2"E")/"F" + "x"` = 0