Just execute a command, which is related to your Activate menu item:
// Obtain IServiceLocator implementer, e.g. from PlatformUI.getWorkbench():
IServiceLocator serviceLocator = PlatformUI.getWorkbench();
// or a site from within a editor or view:
// IServiceLocator serviceLocator = getSite();
ICommandService commandService = (ICommandService) serviceLocator.getService(ICommandService.class);
try {
// Lookup commmand with its ID
Command command = commandService.getCommand("org.eclipse.ui.help.helpContents");
// Optionally pass a ExecutionEvent instance, default no-param arg creates blank event
command.executeWithChecks(new ExecutionEvent());
} catch (ExecutionException | NotDefinedException |
NotEnabledException | NotHandledException e) {
// Replace with real-world exception handling
e.printStackTrace();
}