Final answer:
Ambari is the HDP component that offers a common web UI for managing and monitoring Hadoop clusters, simplifying administration tasks.
Step-by-step explanation:
The Hortonworks Data Platform (HDP) component that provides a common web user interface for applications running on a Hadoop cluster is C) Ambari.
Ambari is designed to make the management and monitoring of Hadoop clusters simpler and more user-friendly. It allows administrators to provision, manage, and monitor a Hadoop cluster, and also to integrate Hadoop with the existing enterprise infrastructure. With Ambari, users can keep track of the various components of the Hadoop ecosystem, such as HDFS, Spark, Hive, and others, making it an integral part of cluster administration.