A boy swings a yo-yo around his head with a force of 50N what is the gravitational force of the yo-yos mass and distance is doubled

Please check for typos and if you have presented the entire problem

Obviously if you double the mass you double the gravitational force.
Now do you maintain the same angle of the circumference to the hand?
do you still have 50 N or do you have a new angle and rotational speed?

60

To find the gravitational force of the yo-yo when its mass and distance are doubled, we first need to understand the equation for gravitational force.

The equation for gravitational force is given by:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.674 * 10^-11 N * m^2 / kg^2)
m1 and m2 are the masses of the objects (in this case, the yo-yo and the Earth)
r is the distance between the centers of the two masses

In this case, we are doubling both the mass and the distance. Let's denote the original mass of the yo-yo as m1 and the original distance as r.

The new mass of the yo-yo will be 2 * m1, and the new distance will be 2 * r.

So, to find the new gravitational force, we can substitute these values into the equation:

F_new = (G * (2 * m1) * m2) / (2 * r)^2

Since we are only interested in finding the new gravitational force value and not its actual numerical value, we can simplify the equation:

F_new = (G * 2 * m1 * m2) / (4 * r^2)

As we can see, the gravitational force is directly proportional to the mass and inversely proportional to the square of the distance. When both the mass and distance are doubled, the gravitational force will be increased by a factor of 2.

Therefore, if the original gravitational force was 50N, the new gravitational force when the mass and distance are doubled would be 100N.