A body of volume 100 cm3 weighs 5 kgf in air. It is completely immersed in a liquid of density
1.8 x 103 kg m-3
. Find:

(i) The upthrust due to liquid and (ii) The weight of the body in liquid.

We are given the following information:

- Volume of the body \( V = 100 \, \text{cm}^3 = 100 \times 10^{-6} \, \text{m}^3 = 1 \times 10^{-4} \, \text{m}^3 \)
- Weight of the body in air \( W = 5 \, \text{kgf} \)
- Density of the liquid \( \rho_{\text{liquid}} = 1.8 \times 10^3 \, \text{kg/m}^3 \)
- Acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \)

### (i) The upthrust due to the liquid

Upthrust (or buoyant force) is given by Archimedes' principle, which states that the upthrust is equal to the weight of the liquid displaced by the body. The formula for upthrust \( F_b \) is:

\[
F_b = \text{Volume of body} \times \text{Density of liquid} \times g
\]

Substitute the known values:

\[
F_b = V \times \rho_{\text{liquid}} \times g
\]
\[
F_b = (1 \times 10^{-4}) \times (1.8 \times 10^3) \times 9.8
\]

Let's calculate the upthrust.

### (ii) The weight of the body in the liquid

The weight of the body in the liquid is the actual weight of the body in air minus the upthrust. Mathematically:

\[
W_{\text{liquid}} = W_{\text{air}} - F_b
\]

We can calculate the weight in the liquid after determining the upthrust. I'll calculate both values now.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the calculations if you want to solve it manually. Would you like me to do that?

Meanwhile, here are 5 questions related to this concept:

1. What is Archimedes' principle and how is it applied in different situations?
2. How does density affect the buoyant force experienced by an object?
3. What is the difference between weight and mass when considering forces in fluids?
4. How does the acceleration due to gravity impact the weight of an object in different fluids?
5. How can you determine if an object will float or sink in a given liquid?

**Tip:** Always ensure units are consistent when performing calculations involving forces and fluid mechanics.

A body of volume 100 cm3 weighs 5 kgf in air. It is completely immersed in a liquid of density 1.8 x 103 kg/m^3. Find: (i) The upthrust due to liquid and (ii) The weight of the body in liquid.

Solve a physics problem where a body of volume 100 cm3 weighs 5 kgf in air and is immersed in a liquid with a density of 1.8 x 103 kg/m^3. Learn how to calculate the upthrust using Archimedes' principle and find the weight of the body in the liquid. Suitable for Grades 10-12.

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