Some iron beads are embedded in wax ball which is just floating in water. The volume of ball is 18 `cm^(3)` and relative density of waxis 0.9 .Then mass of the iron trapped in the ball is

Options

A. 1.8 g
B. 2.7 g
C. 16.8 g
D. 8.1 g

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the Mass of the Wax
The mass of the wax can be calculated using the formula:
\[ \text{Mass of wax} = \text{Volume of ball} \times \text{Relative density of wax} \]
Given:
- Volume of the ball, \( V = 18 \, \text{cm}^3 \)
- Relative density of wax, \( \text{RD} = 0.9 \)

Substituting the values:
\[ \text{Mass of wax} = 18 \, \text{cm}^3 \times 0.9 = 16.2 \, \text{g} \]

### Step 2: Apply the Law of Floatation
According to the law of floatation, the weight of the floating object (in this case, the wax ball with iron beads) is equal to the upthrust (buoyant force) acting on it.

The weight of the ball can be expressed as:
\[ \text{Weight of ball} = (\text{Mass of wax} + \text{Mass of iron}) \times g \]
The upthrust can be expressed as:
\[ \text{Upthrust} = \text{Volume of ball} \times \text{Density of water} \times g \]
Given that the density of water, \( \rho = 1 \, \text{g/cm}^3 \):
\[ \text{Upthrust} = 18 \, \text{cm}^3 \times 1 \, \text{g/cm}^3 \times g = 18g \]

### Step 3: Set Up the Equation
From the law of floatation, we can equate the weight of the ball to the upthrust:
\[ (\text{Mass of wax} + \text{Mass of iron}) \times g = 18g \]
Dividing both sides by \( g \):
\[ \text{Mass of wax} + \text{Mass of iron} = 18 \]

### Step 4: Substitute the Mass of Wax
Now, substituting the mass of wax calculated in Step 1:
\[ 16.2 + \text{Mass of iron} = 18 \]

### Step 5: Solve for the Mass of Iron
Rearranging the equation to find the mass of iron:
\[ \text{Mass of iron} = 18 - 16.2 = 1.8 \, \text{g} \]

### Final Answer
The mass of the iron trapped in the ball is \( 1.8 \, \text{g} \).

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