Re: static_cast and dynamic_cast

#include <iostream>
using namespace std;

class X{
     public:
     virtual void f(){}

};

class Y {
     public:
     virtual void g() {}

};

int main()
{
     X * x = new X();
     Y* y = dynamic_cast<Y*>(x); //A
     // Y* y = static_cast<Y*>(x); //B
     cout << y << endl;

}

When I try to typecast an unrelated class(not in its inheritance
hierarchy) into another as in the above example,
using a static_cast (line B) I get a compile time error. Whereas with
dynamic_cast the code compiles just fine.
I am curious why doesn't the compiler give a compile type error also
in the case of dynamic_cast?