The volume of 500 g sealed packet is 350 `cm^3`. Will the packet float or sink if the density of water is `1(g)/(cm^3)`? What will be the mass of the water displaced by this packed?

Explanation

To determine whether the sealed packet will float or sink in water, and to find the mass of the water displaced by the packet, we can follow these steps:

### Step 1: Identify the Given Values
- Mass of the packet (m_packet) = 500 g
- Volume of the packet (V_packet) = 350 cm³
- Density of water (ρ_water) = 1 g/cm³

### Step 2: Calculate the Density of the Packet
The formula for density (ρ) is given by:

\[ \rho = \frac{m}{V} \]

Where:
- \( m \) = mass
- \( V \) = volume

Substituting the values for the packet:

\[ \rho_{packet} = \frac{500 \, \text{g}}{350 \, \text{cm}^3} \]

Calculating this gives:

\[ \rho_{packet} = \frac{500}{350} \approx 1.43 \, \text{g/cm}^3 \]

### Step 3: Compare Densities
Now, we compare the density of the packet with the density of water:

- Density of the packet (1.43 g/cm³) > Density of water (1 g/cm³)

Since the density of the packet is greater than the density of water, the packet will **sink**.

### Step 4: Calculate the Mass of Water Displaced
According to Archimedes' principle, the mass of water displaced by an object submerged in a fluid is equal to the mass of the fluid that occupies the volume of the object.

The mass of the water displaced can be calculated using the formula:

\[ \text{Mass of water displaced} = \text{Density of water} \times \text{Volume of packet} \]

Substituting the values:

\[ \text{Mass of water displaced} = 1 \, \text{g/cm}^3 \times 350 \, \text{cm}^3 = 350 \, \text{g} \]

### Final Answers
- The packet will **sink**.
- The mass of the water displaced by the packet is **350 g**.

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