A body weight 45 kg wt on the surface of earth. Its weight on the surface of Mars will be
[Mass of Mars = (1/9) mass of earth, Radius of Mars = (1/2) Radius of earth]

Options

A. 25 kg wt
B. 20 kg wt
C. 30 kg wt
D. 40 kg wt

Explanation

To find the weight of a body on the surface of Mars given its weight on Earth, we can follow these steps:

### Step 1: Understand the relationship between weight, mass, and gravity
The weight \( W \) of an object is given by the formula:
\[ W = mg \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity.

### Step 2: Calculate the weight on Earth
Given that the weight of the body on the surface of Earth is 45 kg wt, we can express this as:
\[ W_E = 45 \, \text{kg wt} = 45g_E \]
where \( g_E \) is the acceleration due to gravity on Earth.

### Step 3: Use the relationship for gravity on Mars
The acceleration due to gravity on Mars \( g_M \) can be expressed in terms of the mass and radius of Mars compared to Earth:
\[ g_M = \frac{G M_M}{R_M^2} \]
where \( M_M \) is the mass of Mars and \( R_M \) is the radius of Mars.

### Step 4: Substitute the values for Mars
We know:
- The mass of Mars \( M_M = \frac{1}{9} M_E \)
- The radius of Mars \( R_M = \frac{1}{2} R_E \)

Substituting these into the equation for \( g_M \):
\[ g_M = \frac{G \left(\frac{1}{9} M_E\right)}{\left(\frac{1}{2} R_E\right)^2} \]
This simplifies to:
\[ g_M = \frac{G \left(\frac{1}{9} M_E\right)}{\frac{1}{4} R_E^2} = \frac{4G M_E}{9 R_E^2} = \frac{4}{9} g_E \]

### Step 5: Calculate the weight on Mars
Now, we can find the weight of the body on Mars using the formula:
\[ W_M = mg_M \]
Substituting \( g_M \):
\[ W_M = m \left(\frac{4}{9} g_E\right) \]
Since \( W_E = mg_E = 45 \, \text{kg wt} \), we can express \( m \) as:
\[ m = \frac{W_E}{g_E} = \frac{45}{g_E} \]
Thus,
\[ W_M = \left(\frac{45}{g_E}\right) \left(\frac{4}{9} g_E\right) = 45 \cdot \frac{4}{9} = 20 \, \text{kg wt} \]

### Final Answer
The weight of the body on the surface of Mars is:
\[ \boxed{20 \, \text{kg wt}} \]