Two stones each of mass 5kg fall on a wheel from a height of 10m. The wheel stirs 2kg water. The rise in temperature of water would be

The correct option is 0.12° C.

To find the rise in temperature of the water, we apply the principle of conservation of energy. The potential energy of the falling stones is converted entirely into heat energy, which is absorbed by the water.

Step 1: Calculate the loss in potential energy of the falling stones
The total mass of the stones is the number of stones multiplied by the mass of each stone:
$m=2\times 5\text{kg}=10\text{kg}$
The potential energy ($U$) lost by the stones when they fall from a height ($h$) of 10 m is given by:
$U=m\cdot g\cdot h$
Using the acceleration due to gravity $g=9.8{\text{m/s}}^2$:
$U=10\text{kg}\times 9.8{\text{m/s}}^2\times 10\text{m}=980\text{J}$

Step 2: Relate the mechanical energy to heat energy absorbed by the water
Assuming all of this mechanical energy is converted into heat ($Q$):
$Q=U=980\text{J}$
The heat energy absorbed by the water is given by the formula:
$Q=m_w$
Where:

• $m_w=2\text{kg}$ is the mass of the water.
• $c=4200\text{J/(kg}\cdot \text{°C)}$ is the specific heat capacity of water.
• $\Delta T$ is the rise in temperature.

Step 3: Solve for the rise in temperature ($\Delta T$)
Substitute the known values into the equation:
$980=2\times 4200\times \Delta T$
Simplify and solve for $\Delta T$:
$980=8400\cdot \Delta T$
$\Delta T=\frac{980}{8400}$
$\Delta T\approx 0.1167\text{°C}\approx 0.12\text{°C}$

Thus, the temperature of the water rises by approximately 0.12° C.