A body weighs `700gm` wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass is `1/7` and radius is half that of the earth

Options

A. `200gm wt`
B. `400gm wt`
C. `50gm wt`
D. `300gm wt`

Explanation

To find the weight of a body on the surface of a different planet, we can use the formula for gravitational force, which is given by:

\[ F = m \cdot g \]

where:
- \( F \) is the weight of the body,
- \( m \) is the mass of the body,
- \( g \) is the acceleration due to gravity.

### Step 1: Identify the weight of the body on Earth
The weight of the body on the surface of the Earth is given as \( 700 \, \text{g} \).

### Step 2: Determine the mass of the body
Since weight \( F = m \cdot g \), we can express the mass \( m \) of the body in terms of its weight on Earth. The acceleration due to gravity on Earth is approximately \( g_e = 9.8 \, \text{m/s}^2 \). However, for this problem, we will just use the weight directly.

### Step 3: Calculate the acceleration due to gravity on the new planet
The formula for the acceleration due to gravity \( g \) on the surface of a planet is:

\[ g_p = \frac{G \cdot M_p}{R_p^2} \]

where:
- \( G \) is the universal gravitational constant,
- \( M_p \) is the mass of the new planet,
- \( R_p \) is the radius of the new planet.

Given:
- The mass of the new planet \( M_p = \frac{1}{7} M_e \) (where \( M_e \) is the mass of Earth),
- The radius of the new planet \( R_p = \frac{1}{2} R_e \) (where \( R_e \) is the radius of Earth).

Substituting these values into the formula for \( g_p \):

\[ g_p = \frac{G \cdot \left(\frac{1}{7} M_e\right)}{\left(\frac{1}{2} R_e\right)^2} \]

\[ g_p = \frac{G \cdot \left(\frac{1}{7} M_e\right)}{\frac{1}{4} R_e^2} \]

\[ g_p = \frac{4G \cdot M_e}{7R_e^2} \]

### Step 4: Relate \( g_p \) to \( g_e \)
We know that:

\[ g_e = \frac{G \cdot M_e}{R_e^2} \]

Thus, we can express \( g_p \) in terms of \( g_e \):

\[ g_p = \frac{4}{7} g_e \]

### Step 5: Calculate the weight of the body on the new planet
Now we can find the weight of the body on the new planet:

\[ F_p = m \cdot g_p \]

Since \( F_e = m \cdot g_e = 700 \, \text{g} \), we can express \( m \) as:

\[ m = \frac{700 \, \text{g}}{g_e} \]

Now substituting for \( F_p \):

\[ F_p = \left(\frac{700 \, \text{g}}{g_e}\right) \cdot \left(\frac{4}{7} g_e\right) \]

\[ F_p = 700 \cdot \frac{4}{7} \]

\[ F_p = 400 \, \text{g} \]

### Final Answer
The weight of the body on the surface of the new planet is **400 grams**.

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