error: 'Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)' after changing path of data dir

Question

I am using mysql 5.6. I wanted to change the data directory for my database. So did following steps -

1. copy whole mysql folder from /var/lib/mysql/ to new folder named app.

2. Then grant permission to that folder.

3. stop mysql server.

4. changes in my.cnf for datadir =/app/mysql and socket variable = /app/mysql/mysql.sock

5. restart the server.

Now when I am trying to run mysql -uroot -proot it gives me following error -

'Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)'

But when I can log in using following -

mysql -uroot -proot -h 127.0.0.1 or my system's IP or --socket =  /app/mysql/mysql.sock

Please let me know what I have missed.

EDIT: When I am commenting socket variable in my.cnf. It is accessing mysql.sock from old path but working fine.

# socket = /app/mysql/mysql.sock

Is it correct to use it or I have to use from same data dir?