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The correct option is;

The assertion is correct, but reason wrong

Explanation:

The question is with regards to the relationship between work, energy, power, and velocity

The mass of each of the persons running up the staircase = Different

The time it takes each person to run up the stairs = Equal time

Let, 'm₁' and 'm₂' represent the mass of each of the persons that ran up the stairs and m₁ > m₂

Let 't' represent the equal time it takes then to run up the stairs

Let 'h' represent the height of the stairs

The energy, 'E', it takes to run up the stairs is equal to the potential energy, P.E., obtained at the top of the stairs

P.E. = m·g·h

Where;

m = The mass of the person at an elevated height

g = The acceleration due to gravity = Constant

h = The height reached above ground level

Given that the height reached is the same for both of the persons, we have

For m₁, P.E.₁ = m₁·g·h and for m₂, P.E.₂ = m₂·g·h

Therefore, where, m₁ > m₂, we have;

P.E.₁ > P.E.₂

∴ E₁ > E₂

Power, 'P', is the rate at which energy is expended

∴ Power, P = E/t

∴ P₁ = E₁/t  > P₂ = E₂/t

Therefore, the person with the greater mass, 'm₁', uses more power than the person of mass 'm₂', in running up the stairs

Therefore, the assertion is correct

The average velocity, vₐ = (Total distance traveled, d)/(Total time taken, t)

Given that the distance, 'd', covered in running up the stairs by both persons is the same, and the time it takes them to complete the distance, 't', is also the same, we have;

The average velocity of the person with the greater mass m₁ is the same as the average velocity of the person with mass, m₂

Therefore, the reason is wrong

The answer is that the assertion is correct, but reason wrong

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.

365.25 earth days are in the year of a light year