How to provide a access to the data base if the user is not having the privilleges In MS SQL Server
2008 R2 is installed by a user "A" and he has a data base named "DB1" . He left the company. Now the user "B" is trying to access the data base. He is able to see the data abse and but he is not having the privillege to read the data.

We don know the password of sql authentication. Both users are tin the admin group in that machine where the sql server is installed .

now is there any way by which the user is able to read the data
With SQL Server 2008 onward local Windows Administrators are not added as SQL Server Administrators by default.

If you do not have access to any Administrative account to SQL Server then you need to start SQL Server in single user mode, in this mode local Windows Administrators can login to SQL Server. Once logged in you can create a new Administrative Account.

Refer link for step by step tutorial: SQL Server – How to connect to SQL Server when ‘sa’ account is disabled