Your spaceship lands on an unknown planet. To determine the characteristics of this planet, you drop a wrench from 3.50 m above the ground and measure that it hits the ground 0.809 s later. Assuming that the planet has the same density as that of earth (5500 kg/m3), what is the radius of the planet?

Explanation:

By the formula,

where a is the acceleration of objects by gravity.

We also know that by the Law of Gravitation,

The mass of the planet is given by

So

Since R>>3.5, so we approximate

Solving the last equation,

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.