Final answer:
Therefore, the rise in temperature of the water will be approximately 1.4°C. None of the given options (a) 2°C, (b) 4°C, (c) 6°C, (d) 8°C are correct.
Step-by-step explanation:
To find out the rise in temperature of water due to the falling masses, we can use the principle of conservation of energy. Specifically, the potential energy lost by the falling masses is converted into heat energy (thermal energy), which is then absorbed by the water causing an increase in temperature.
First, we calculate the total potential energy (PE) of the two masses at height (h):
PE = m × g × h × 2 (since there are two masses),
where m = mass of one object, g = acceleration due to gravity (9.81 m/s²), and h = height.
For two 5 kg masses falling from 10 m:
PE = 5 kg × 9.81 m/s² × 10 m × 2 = 981 J × 2 = 1962 J.
This energy is completely transferred to the water, raising its temperature. The specific heat capacity of water is 4.186 J/g°C (or 4186 J/kg°C), and we have 2 kg of water.
Using the formula q = mcΔT, where q is the heat absorbed, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature, we find:
ΔT = q / (mc) = 1962 J / (2 kg × 4186 J/kg°C) ≈ 0.234°C
However, this answer is surprisingly low because we would expect the gravitational potential energy of the falling masses to produce a higher temperature rise. It is possible that there is an error in the given values or the calculations, which should be checked.