Question

The mass of a spherical planet is 4 times the mass of the earth, but its radius ($R$) is same as that of the earth. How much work is done in lifting a body of mass 5 kg through a distance of 2 m on the planet? ($g = 10\ \text{ms}^{-2}$)

• A. $400\ \text{J}$
• B. $200\ \text{J}$
• C. $800\ \text{J}$
• D. $300\ \text{J}$

Hint:

Since planetary radius is unchanged, gravity scales linearly with the planet's mass. Because the planet is 4 times heavier, the surface gravity is 4 times stronger, meaning it requires exactly 4 times more work than it would on Earth ($W_{\text{Earth}} = 5 \times 10 \times 2 = 100\ \text{J} \rightarrow W_{\text{Planet}} = 400\ \text{J}$).

Answer 1

The Correct Option is A

Step 1: Understand the setup.
A planet has $4$ times Earth's mass but the same radius. We must find the work to raise a $5\,\text{kg}$ body by $2\,\text{m}$ on this planet.
Step 2: Note how surface gravity depends on mass and radius.
Surface gravity is $g = \dfrac{GM}{R^2}$, so for fixed radius the gravity scales directly with the mass.
Step 3: Scale the gravity for the planet.
Mass becomes $4$ times and $R$ is unchanged, so the new gravity is $g' = 4g = 4 \times 10 = 40\,\text{m s}^{-2}$.
Step 4: Recall the work-against-gravity formula.
Lifting a mass $m$ slowly through height $h$ stores potential energy, so the work done is $W = m g' h$.
Step 5: Put in the numbers.
$W = 5 \times 40 \times 2$.
Step 6: Evaluate.
$W = 400\,\text{J}$, matching option (1).
\[ \boxed{W = 400\ \text{J}} \]