How dare people on here call you a troll. You are totally believable. I'm not muslim, but I am a teacher with a strong interest in psychology, and I can well believe that your mum might do this - sick though it is. I know what you mean about thinking that anything you do will only make things worse - but you have to feel like you've tried something! I'm sad to say this, but I think your older sister has become accustomed to institutional bullying in your household, and has therefore become part of the system. This does, however, reflect well on you, because you've not done this. You've not had your mind twisted into thinking that it's ok to beat a little girl. Your post on here could be the start of a process that ends with your sister being saved - IF YOU TAKE ACTION! But if you don't, and the abuse continues - then you run the risk of your little sister turning out the same as your older sister.
You should secretly tell somebody at your sister's school. All schools have a person designated to deal with child protection issues. In primary schools, this is almost always the headteacher. Ring them up, and make an appointment to see them - don't tell them all the details over the phone. If you report to the headteacher you must firstly write down the details. Write down everything that has happened, quote your mother in her tirades. Quote your sister, though you MUSTN'T at all costs ask her any 'leading questions' such as 'how does this make you feel', or 'I bet you don't like that, do you?'. This is really important. Just let her tell you things as she likes. DO NOT tell her that you're going to go into her school, though. The designated child protection person will keep all information strictly confidential, unless they think they have to tell authorities. but most likely, they will simply keep a closer eye on your sister, and if anyone makes any further statements with regards to her, then things will be taken further. Your mum will not be informed that you have made contact.