A 42 kg block of ice moving on rough horizontal surface stops due to friction, after sometime. If the initial velocity of the decelerating block is `4ms^-1`, the mass of ice (in kg) that has melted due to the heat generated by the friction is (Latent heat of ice is `3.36xx10^5Jkg^ -1`

Options

A. `1xx10^-3`
B. `1.5xx10^-3`
C. `2xx10^-3`
D. `2.5xx10^-3`

Answer

To solve the problem, we need to find the mass of ice that melts due to the heat generated by the friction when a 42 kg block of ice moving at an initial velocity of 4 m/s comes to a stop.

### Step-by-step solution:

1. **Calculate the initial kinetic energy (KE) of the block of ice**:
The formula for kinetic energy is given by:
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is the mass and \( v \) is the velocity.

Substituting the given values:
\[ KE = \frac{1}{2} \times 42 \, \text{kg} \times (4 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 42 \times 16 \]
\[ KE = 21 \times 16 = 336 \, \text{J} \]

2. **Relate the kinetic energy to the heat absorbed by the ice**:
The heat generated by friction is absorbed by the ice and causes it to melt. The heat absorbed (Q) can be expressed in terms of the mass of ice melted (m) and the latent heat of fusion (L):
\[ Q = m \cdot L \]
where \( L \) is the latent heat of ice, given as \( 3.36 \times 10^5 \, \text{J/kg} \).

3. **Set the kinetic energy equal to the heat absorbed**:
Since all the kinetic energy is converted into heat:
\[ KE = m \cdot L \]
Substituting the values we have:
\[ 336 \, \text{J} = m \cdot (3.36 \times 10^5 \, \text{J/kg}) \]

4. **Solve for the mass of ice melted (m)**:
Rearranging the equation gives:
\[ m = \frac{336 \, \text{J}}{3.36 \times 10^5 \, \text{J/kg}} \]
\[ m = \frac{336}{336000} = 0.001 \, \text{kg} \]

5. **Convert the mass to grams if necessary**:
\[ m = 0.001 \, \text{kg} = 1 \, \text{g} \]

Thus, the mass of ice that has melted due to the heat generated by the friction is **0.001 kg** or **1 gram**.