The weight of a body A on the surface of the earth is equal to the weight of the body B on the surface of moon, the ratio of the mass of A to that of B is________ [The acceleration due to gravity on the surface of earth is six times the acceleration due to gravity on the surface of moon].

Options

A. ` 1: 1`
B. ` 1 : 6`
C. ` 6 : 1`
D. ` 1 : 2`

Explanation

To solve the problem, we need to find the ratio of the mass of body A (on Earth) to the mass of body B (on the Moon) given that their weights are equal and the acceleration due to gravity on Earth is six times that on the Moon.

### Step-by-step Solution:

1. **Understand the Weight Formula**:
The weight of an object is given by the formula:
\[ \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \]
Therefore, the weight of body A on Earth can be expressed as:
\[ W_A = M_A \times g_E \]
where \( M_A \) is the mass of body A and \( g_E \) is the acceleration due to gravity on Earth.

2. **Weight of Body B on the Moon**:
Similarly, the weight of body B on the Moon can be expressed as:
\[ W_B = M_B \times g_M \]
where \( M_B \) is the mass of body B and \( g_M \) is the acceleration due to gravity on the Moon.

3. **Set the Weights Equal**:
According to the problem, the weights of body A and body B are equal:
\[ M_A \times g_E = M_B \times g_M \]

4. **Substitute the Relationship of Gravity**:
We know from the problem that the acceleration due to gravity on Earth is six times that on the Moon:
\[ g_E = 6 \times g_M \]
Substitute this into the equation:
\[ M_A \times (6 \times g_M) = M_B \times g_M \]

5. **Simplify the Equation**:
We can cancel \( g_M \) from both sides (assuming \( g_M \neq 0 \)):
\[ 6 \times M_A = M_B \]

6. **Find the Ratio of Masses**:
To find the ratio of the mass of A to the mass of B, we rearrange the equation:
\[ \frac{M_A}{M_B} = \frac{1}{6} \]
Therefore, the ratio of the mass of A to the mass of B is:
\[ M_A : M_B = 1 : 6 \]

### Final Answer:
The ratio of the mass of A to that of B is \( 1 : 6 \).

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