C. tcpdump
When investigating why users cannot reach a Linux web server with a browser but can ping the server IP, the administrator should run the tcpdump command on the server first. Tcpdump is a packet analyzer that allows the administrator to capture and analyze network traffic in real-time. By running tcpdump, the administrator can inspect the packets arriving at the server, which can provide insights into whether the server is receiving HTTP traffic and whether there are any issues with the communication.
Options A (traceroute), B (netstat), and D (arp) are useful for different purposes but may not directly help diagnose the issue at hand. Traceroute shows the path taken by packets, netstat displays network statistics and connections, and arp resolves IP addresses to MAC addresses. Tcpdump is better suited for capturing and analyzing the actual traffic arriving at the server, helping identify potential issues with web traffic.