Physics Q32 – JEE-MAIN 2026

A body of mass

m

is taken from the surface of earth to a height equal to twice the radius of earth (

R_{e}

). The increase in potential energy will be _______. (

g

is acceleration due to gravity at the surface of earth)

Clue 1 of 3: Gravitational Potential Energy

Recall the formula for gravitational potential energy of a mass $m$ at a distance $r$ from the center of a planet of mass $M$ .

🧠 Full Solution Path

Step 1: Identify Initial and Final Positions✦ Active

The body starts at the Earth's surface, so its initial distance from the Earth's center is $r_{1} = R_{e}$ . It is moved to a height $h = 2 R_{e}$ from the surface, so its final distance from the Earth's center is $r_{2} = R_{e} + h = R_{e} + 2 R_{e} = 3 R_{e}$ .

Step 2: Calculate Potential Energy at Each Position○ Expand

The gravitational potential energy of a mass $m$ at a distance $r$ from the center of Earth (mass $M$ ) is given by $U = - \frac{G M m}{r}$ .

U_{1} = - \frac{G M m}{R_{e}}

U_{2} = - \frac{G M m}{3 R_{e}}

💡 Teacher's Secret Hint

Remember that gravitational potential energy is negative and increases (becomes less negative) as distance from the center increases.

Step 3: Determine the Increase in Potential Energy○ Expand

The increase in potential energy is $Δ U = U_{2} - U_{1}$ . We also know that the acceleration due to gravity at the surface is $g = \frac{G M}{R_{e}^{2}}$ , which implies $G M = g R_{e}^{2}$ .

Δ U = - \frac{G M m}{3 R_{e}} - (- \frac{G M m}{R_{e}}) = \frac{G M m}{R_{e}} - \frac{G M m}{3 R_{e}}

Δ U = G M m (\frac{1}{R_{e}} - \frac{1}{3 R_{e}}) = G M m (\frac{3 - 1}{3 R_{e}}) = \frac{2 G M m}{3 R_{e}}

Substitute $G M = g R_{e}^{2}$ into the expression for $Δ U$ :

Δ U = \frac{2 (g R_{e}^{2}) m}{3 R_{e}} = \frac{2 m g R_{e}^{2}}{3 R_{e}} = \frac{2}{3} m g R_{e}

💡 Teacher's Secret Hint

Ensure correct algebraic manipulation of fractions and substitution of $G M$ in terms of $g$ and $R_{e}$ .

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 32 – JEE-MAIN 2026

Clue 1 of 3: Gravitational Potential Energy

🧠 Full Solution Path