This is from the RVM documentation for several custom installations:
However, once the installation is complete, and the following instructions for adding users to the rvm group, using sudo or rvmsudo is no longer required. The sudo command is intended only to temporarily elevate privileges so that the installer can shut down. If you need to use "sudo" or "rvmsudo" after the installation is complete, some of the installation instructions have not been properly followed. This usually happens because people perform the installation as root rather than follow the installation instructions from a user account without privileges.
Those last two sentences are very important.
RVM is intended to be used as a single-user tool installed in their home directory, and if it is installed this way, NEVER need sudo to run or install or modify anything, or when the user will never do anything as root .
The Installation Troubleshooting section of the installation documentation page is a good starting point for you.
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