When you first time apply electric to system Mpu6050 opens in sleep mode. You need to wake up the sensor. This code is from my own library and it works fine.

In first line I write "0" in "power management 1" register for wake up the sensor. After that communication starts and internal sensors (gyro + accelerometer) starts working.

void MPU6050::config(){
    write_byte(MPU6050_ADDR0, MPU6050_PWR_MGMT1, 0);                //Mpu6050 outoff the sleep mode
    write_byte(MPU6050_ADDR0, MPU6050_CONFIG, 0x02);                        //Mpu6050 low pass filter set to 3ms
    write_byte(MPU6050_ADDR0, MPU6050_ACCEL_CONF, accel_fs_reg);            //Mpu6050 Accel Set to 2g mode default
    write_byte(MPU6050_ADDR0, MPU6050_GYRO_CONF,  gyro_fs_reg);             //Mpu6050 Gyro  Set to 250 degre/sec default
    delay(30);                                                              //For Gyroscope Startup Time
}