There are many ways to hide ribbon control in SharePoint 2010.
By using the Security Trimmer control. The Security Trimmer control can be place around the ribbon in Master page.The PermissionString attribute value can be changed based on the requirement.
<SharePoint:SPSecurityTrimmedControl PermissionsString="ManagePermissions" runat="server">
<div id="s4-ribbonrow" class="s4-pr s4-ribbonrowhidetitle">
</div>
</SharePoint:SPSecurityTrimmedControl>
S4-ribbonrow corresponds to ribbon in SharePoint 2010 and 2013 as well. In the permissionString give the appropriate permissions.
Happy Share Pointing :-)