Rankers Physics
Topic: Thermal Physics
Subtopic: Calorimetry

A block of mass 20 Kg, fall from a height of 20m. After colliding with ground 75% of energy goes in raising temperature of block. Find rise in temperature of block? (Take specific heat of block 100 J/Kg°C) :
1/2°C
1.5°C
2°C
1°C

Solution:

To find the rise in temperature of the block, we can follow these steps:

1. Calculate the potential energy of the block before it falls:
\[
\text{Potential energy} = m \times g \times h
\]
where:
- \( m = 20 \, \text{kg} \) (mass of the block)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 20 \, \text{m} \) (height)

\[
\text{Potential energy} = 20 \times 10 \times 20 = 4000 \, \text{J}
\]

2. Energy converted to heat:
Since 75% of the energy goes into raising the temperature of the block:
\[
\text{Heat energy} = 0.75 \times 4000 = 3000 \, \text{J}
\]

3. Use the heat energy to calculate the rise in temperature:
The formula for heat energy is:
\[
Q = m \times c \times \Delta T
\]
where:
- \( Q = 3000 \, \text{J} \) (heat energy)
- \( m = 20 \, \text{kg} \)
- \( c = 100 \, \text{J/kg°C} \) (specific heat of the block)
- \( \Delta T \) is the rise in temperature (to be found)

Rearranging the formula to solve for \( \Delta T \):
\[
\Delta T = \frac{Q}{m \times c} = \frac{3000}{20 \times 100} = \frac{3000}{2000} = 1.5^\circ \text{C}
\]

Thus, the rise in temperature of the block is 1.5°C.

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