Static Mutex for Class member Function : C++ 11

Referring to RAII

I can use static mutex for a critical section as:

#include <string>
#include <mutex>
#include <iostream>
#include <fstream>
#include <stdexcept>

void write_to_file (const std::string & message) {
    // mutex to protect file access
    static std::mutex mutex;

    // lock mutex before accessing file
    std::lock_guard<std::mutex> lock(mutex);

    // try to open file
    std::ofstream file("example.txt");
    if (!file.is_open())
        throw std::runtime_error("unable to open file");

    // write message to file
    file << message << std::endl;

    // file will be closed 1st when leaving scope (regardless of exception)
    // mutex will be unlocked 2nd (from lock destructor) when leaving
    // scope (regardless of exception)
}

If use the same approach for a class member function such as:

class Test{
public:
void setI(int k)
{
static std::mutex mutex;
std::lock_guard<std::mutex> lock(mutex);
i=k;
}

private:
int i;

};

What are the cons and pros of above approach?

Is it more advisable to use the approach as below:

class Test
{
public:
    void setI(int k)
    {
        std::lock_guard<std::mutex> lock(mutex);
        i = k;
    }

private:
    int i;
    std::mutex mutex;
};

which method to ensure thread safety is better?