Answer:
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
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