A solid weighs 4.8g in air, 2.8g in water and 3.2g in Kerosine. The ratio of density of the solid to that of the kerosine is

1. Analyze the Question

We are given the weight of a solid in three different media: air, water, and kerosene. We need to find the ratio of the density of the solid to the density of kerosene.

Given:

• Weight of solid in air ($W_a$) = 4.8 g
• Weight of solid in water ($W_w$) = 2.8 g
• Weight of solid in kerosene ($W_k$) = 3.2 g

2. Explain the Concept

The density of a substance relative to a liquid can be determined using the principle of upthrust (Archimedes' Principle).

• Upthrust in a liquid = Weight in air - Weight in liquid.
• Relative Density (RD) of a solid = $\frac{\text{Weight in air}}{\text{Loss of weight in water}}$ (if comparing to water).
• More generally, the ratio of the density of a solid ($\rho_s$) to the density of a liquid ($\rho_l$) is given by: $$\frac{\rho_s}{\rho_l} = \frac{\text{Weight of solid in air}}{\text{Loss of weight in liquid}}$$ Where the "Loss of weight in liquid" is the upthrust provided by that specific liquid.

3. Show the Solution

Step 1: Calculate the loss of weight of the solid in kerosene. The loss of weight in kerosene is the difference between the weight in air and the weight in kerosene:

Step 2: Use the density ratio formula. The ratio of the density of the solid ($\rho_s$) to the density of kerosene ($\rho_k$) is the ratio of the weight of the solid in air to the upthrust (loss of weight) in kerosene:

Step 3: Simplify the fraction.

4. Identify the Answer

The calculation gives us 3. Comparing this to the provided options: A. 2 B. 3/2 C. 2/3 D. 3

The correct option is D.

5. Tip

When solving "weight in liquid" problems, always remember that the loss of weight is equal to the weight of the liquid displaced. If you are asked for the density of the liquid itself, you can use the ratio of the loss of weight in that liquid to the loss of weight in water!