I am able to browse google sites and can access the internet but not able to ping WWW.GOOGLE.COM

It would be common to allow you to be able to ping machine that were inside your company network but not those outside. Really the only way you are going to find the answer is to get into the router/firewall going to the internet and see if there are restrictions configured.

It could also be the firewall settings on the PC itself. If it get into the wrong type of network it will restrict certain types of traffic.
 


That's absolutely right.

OP, why do you need to be able to ping Google from your work computer? I'm a Network Administrator and disabling ICMP requests outside the LAN is very common. The most likely reason why it works within the LAN is for troubleshooting purposes, so your IT team can establish the quality of your computer's network connection.