Benzyl Carbocation Stability: Would electron-withdrawing group on the ring destabilize the carbocation?
The reaction shown here is a Finkelstein reaction and SN2 reaction mechanism is followed.is an organic reaction that uses an alkyl halide exchange into another alkyl halide through a reaction wherein the metal halide salt is used. This reaction takes place at an equilibrium process by taking the advantage of poor acetone solubility in metal halide salt that is newly formed. The mechanism of the Finkelstein reaction is single-step SN2 reaction with stereochemistry inversion.

The success of this reaction depends on the below conditions.


Nucleophilicity of your halogen
Nature of leaving group
Carbon-halogen bond 
Alkyl Halide reactivity


Holtz and Stock showed that electron-withdrawing groups increase the rate of SN2 reactions. This can be ascribed to stabilization of the transition state by withdrawal of some of the electron density. So NO2 will make reaction faster.

Ref:ADVANCED ORGANIC CHEMISTRY: REACTIONS, MECHANISMS AND STRUCTURE, 4TH ED