I have a linux machine with 2 ethernet ports(eth0 and eth1). eth0 is connected to a router which assigns it an IP address 192.168.1.2. eth1 is connected to a switch which doesn't have an IP. How do I ping eth0 from eth1?
If your eth1 doesnt have an IP, it will not be able to work with IP traffic (and ping / ICMP is IP traffic). Did I misunderstood your problem ?
Edit : I am not sure that I understand your network. Could you send a schema ?
If I understood correctly, you ahve eth0 configured with DHCP and eth1 configured manually. Are you sure that the address you have on eth1 is correct ? If you configured it as 10.0.0.1, you need to have y router with an interface in the same subnet, and the router has to be configured to route trafic from your 192.168.1.0/24 to you 10.0.0.0/24 networks.