A body weighs `50 g` in air and `40 g` in water. How much would it weigh in a liquid of specific gravity `1.5`

Options

A. 65 g
B. 45 g
C. 30 g
D. 35 g

Explanation

To solve the problem of how much a body weighing 50 g in air would weigh in a liquid of specific gravity 1.5, we can follow these steps:

### Step 1: Understand the given data
- Weight of the body in air (W_air) = 50 g
- Weight of the body in water (W_water) = 40 g

### Step 2: Calculate the buoyant force in water
The buoyant force (B) can be calculated using the difference between the weight in air and the weight in water:
\[ B = W_{air} - W_{water} \]
\[ B = 50 \, g - 40 \, g = 10 \, g \]

### Step 3: Determine the volume of the body
Since the buoyant force is equal to the weight of the water displaced, we can find the volume (V) of the body using the density of water (1 g/cm³):
\[ B = \text{Density of water} \times V \times g \]
Here, \( g \) is the acceleration due to gravity, which cancels out when using weights in grams. Thus:
\[ 10 \, g = 1 \, g/cm³ \times V \]
This gives:
\[ V = 10 \, cm³ \]

### Step 4: Calculate the buoyant force in the liquid with specific gravity 1.5
The specific gravity (SG) of the new liquid is given as 1.5, which means its density is:
\[ \text{Density of liquid} = 1.5 \times \text{Density of water} = 1.5 \, g/cm³ \]
Now, we can calculate the buoyant force (B_liquid) in this liquid:
\[ B_{liquid} = \text{Density of liquid} \times V \times g \]
\[ B_{liquid} = 1.5 \, g/cm³ \times 10 \, cm³ = 15 \, g \]

### Step 5: Calculate the weight of the body in the new liquid
The weight of the body in the liquid (W_liquid) can be calculated as:
\[ W_{liquid} = W_{air} - B_{liquid} \]
\[ W_{liquid} = 50 \, g - 15 \, g = 35 \, g \]

### Final Answer
The weight of the body in the liquid of specific gravity 1.5 is **35 g**.

---