  A model for the supercooled liquid is considered by taking into account its
solid like properties. We focus on how the long time dynamics is affected due
to the coupling between the slowly decaying density fluctuations and the local
displacement variables in the frozen liquid. Results from our model agree with
the recent observation of Novikov and Sokolov [Nature (London) {\bf 431}, 961
(2004)] that the fragility index $m$ of a glass forming material is linearly
related to the corresponding ratio $K/G$ of the bulk and the shear moduli.
