How much momentum will a dumb-bell of mass `10kg` transfer to the floor if it falls a height of `80 cm`? Take its downward acceleration to be `10 m//s^(2)`.

Explanation

To find the momentum transferred to the floor by a dumbbell of mass 10 kg falling from a height of 80 cm, we can follow these steps:

### Step 1: Convert the height from centimeters to meters
The height given is 80 cm. We need to convert this to meters for our calculations.
\[ \text{Height (h)} = 80 \text{ cm} = \frac{80}{100} = 0.8 \text{ m} \]

### Step 2: Identify the initial velocity
The dumbbell is falling from rest, so the initial velocity (u) is:
\[ u = 0 \text{ m/s} \]

### Step 3: Use the equation of motion to find the final velocity (v)
We can use the second equation of motion:
\[ v^2 = u^2 + 2as \]
where:
- \( a = 10 \text{ m/s}^2 \) (downward acceleration)
- \( s = 0.8 \text{ m} \) (height fallen)

Substituting the values:
\[ v^2 = 0^2 + 2 \times 10 \times 0.8 \]
\[ v^2 = 0 + 16 \]
\[ v^2 = 16 \]
\[ v = \sqrt{16} = 4 \text{ m/s} \]

### Step 4: Calculate the momentum (p)
Momentum is given by the formula:
\[ p = mv \]
where:
- \( m = 10 \text{ kg} \) (mass of the dumbbell)
- \( v = 4 \text{ m/s} \) (final velocity)

Substituting the values:
\[ p = 10 \times 4 = 40 \text{ kg m/s} \]

### Final Answer
The momentum transferred to the floor by the dumbbell is:
\[ \text{Momentum} = 40 \text{ kg m/s} \]

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