  Recently, Verlinde proposed that gravity is an emergent phenomenon which
originates from an entropic force. In this work, we extend Verlinde's proposal
to accommodate generalized uncertainty principles (GUP), which are suggested by
some approaches to \emph{quantum gravity} such as string theory, black hole
physics and doubly special relativity (DSR). Using Verlinde's proposal and two
known models of GUPs, we obtain modifications to Newton's law of gravitation as
well as the Friedmann equation. Our modification to the Friedmann equation
includes higher powers of the Hubble parameter which is used to obtain a
corresponding Raychaudhuri equation. Solving this equation, we obtain a leading
Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the
$p=\omega \rho$ equation of state.
