In free fall, a body of mass 1kg drops from a height of 125m from rest in 5s. How long will it take another body of mass 2kg to fall from rest from the same...

In free fall, a body of mass 1kg drops from a height of 125m from rest in 5s. How long will it take another body of mass 2kg to fall from rest from the same height? [g = 10ms-1·]

Answer Details

The time taken for an object to fall from a given height in free fall depends only on the height and the acceleration due to gravity. It is independent of the mass of the object. The formula for the time taken for an object to fall from rest from a height h in free fall is given by: t = √(2h/g) where h is the height and g is the acceleration due to gravity. In this question, we are given that a body of mass 1 kg falls from a height of 125 m in 5 s. Using the formula above, we can find the value of g: t = √(2h/g) 5 s = √(2 x 125 m / g) 25 s^2 = 250 m / g g = 250 m / (25 s^2) g = 10 m/s^2 We are then asked to find how long it will take for a body of mass 2 kg to fall from rest from the same height. Using the same formula as before, but with the new value of g, we get: t = √(2h/g) t = √(2 x 125 m / 10 m/s^2) t = √(25) t = 5 s Therefore, it will take the body of mass 2 kg the same amount of time as the body of mass 1 kg to fall from the same height, which is 5 s. The correct option is (a): 5s.