On a planet whose size is the same and mass is 3 times as that of the earth, calculate the energy required to raise a 5kg mass vertically upwars through a distance of 5m.
Take g on earth `= 10 m//s^(2)`

Explanation

To solve the problem of calculating the energy required to raise a 5 kg mass vertically upwards through a distance of 5 m on a planet that has the same size as Earth but is three times as massive, we will follow these steps:

### Step 1: Determine the acceleration due to gravity on the new planet.

The formula for gravitational acceleration \( g' \) on the surface of a planet is given by:
\[ g' = \frac{G \cdot M}{R^2} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.

Since the mass of the new planet is three times that of Earth (\( M' = 3M_e \)) and the radius is the same as Earth (\( R' = R_e \)), we can substitute these values into the formula:
\[ g' = \frac{G \cdot (3M_e)}{R_e^2} = 3 \cdot \frac{G \cdot M_e}{R_e^2} = 3g_e \]
Given that \( g_e = 10 \, \text{m/s}^2 \) (acceleration due to gravity on Earth), we find:
\[ g' = 3 \cdot 10 = 30 \, \text{m/s}^2 \]

### Step 2: Calculate the work done to raise the mass.

The work done \( W \) in raising an object is given by the formula:
\[ W = m \cdot g' \cdot h \]
where:
- \( m \) is the mass (5 kg),
- \( g' \) is the acceleration due to gravity on the new planet (30 m/s²),
- \( h \) is the height (5 m).

Substituting the values:
\[ W = 5 \, \text{kg} \cdot 30 \, \text{m/s}^2 \cdot 5 \, \text{m} \]
Calculating this gives:
\[ W = 5 \cdot 30 \cdot 5 = 750 \, \text{J} \]

### Final Answer:
The energy required to raise a 5 kg mass vertically upwards through a distance of 5 m on the new planet is **750 Joules**.

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