Isn’t this the normal way to free the memory associated with an object?
This is a common way of managing dynamically allocated memory, but it’s not a good way to do so. This sort of code is brittle because it is not exception-safe: if an exception is thrown between when you create the object and when you delete it, you will leak that object.
It is far better to use a smart pointer container, which you can use to get scope-bound resource management (it’s more commonly called resource acquisition is initialization, or RAII).
As an example of automatic resource management:
void test()
{
std::auto_ptr<Object1> obj1(new Object1);
} // The object is automatically deleted when the scope ends.
Depending on your use case, auto_ptr might not provide the semantics you need. In that case, you can consider using shared_ptr.
As for why your program crashes when you delete the object, you have not given sufficient code for anyone to be able to answer that question with any certainty.