A volcanic eruption launches two rocks of different masses into the air. The first rock had a mass of 10 kilograms while the second rock had a mass of 20 kilograms. At the eruption, both rocks accelerated at a rate of 600 m/s2. Which of the following statements is true regarding the eruption of the two rocks?
The amount of force applied to rock one was twice as much as the force applied to rock two during the eruption.
The amount of force applied to rock one was the same as the force applied to rock two during the eruption.
The amount of force applied to rock one was half the amount of force applied to rock two during the eruption.
The amount of force applied to the rocks is impossible to determine without knowing the inertia of the rocks.

The statement that is true regarding the eruptions of the two rocks is;

Option C; The amount of force applied to rock one was half the amount of force applied to rock two during the eruption.

We are given;

Mass of first rock; m1 = 10 kg

Mass of second rock; m2 = 20 kg

Acceleration of both rocks; a = 600 m/s²

The formula for Force applied is;

F = ma

Where;

m is mass

a is acceleration

Now;

Force applied on first rock; F1 = m1 × a

F1 = 10 × 600

F1 = 6000 N

Force applied on second rock; F2 = m2 × a

F2 = 20 × 600

F2 = 12000 N

We can see that the force applied to rock 1 was half the amount of force applied to rock 2.

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C. The amount of force applied to rock one was half the amount of force applied to rock two during the eruption.

Explanation:

A force is an agent which changes the state of an object well applied to it. Second Newton's law of motion state's that;

F = ma

where F is the force, m is the mass of the object and a is the acceleration of the object.

In the given question,

Mass of first rock = 10 kilograms

Mass of the second rock = 20 kilograms

Acceleration of the two rocks = 600 m/

Thus,

Force on the first rock = ma

                                    = 10 x 600

                                    = 6000 N

Force on the second rock = 20 x 600

                                   = 12000 N

Therefore, it can be observed that the amount of force applied to rock one was half the amount of force applied to rock two during the eruption.

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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.