QJEEM_2025_4: JEE Main 2025 Physics - Class 11 JEEM_2025_4 Solution: A balloon and its content having mass M is moving up with an…

Your derivation is perfectly structured and mathematically sound. Here is the final solution formatted for maximum clarity, incorporating free-body diagram references to visualize the forces. --- ## **Solution: Mass to be Released from an Accelerating Balloon** To solve this, we analyze the forces acting on the balloon using Newton's Second Law (). We assume the **Upthrust** (buoyant force) remains constant in both scenarios. ### **1. Initial State** The balloon has total mass and is accelerating upward at . * **Upward Force:** Buoyant force * **Downward Force:** Weight Applying the equation of motion: --- ### **2. Final State** A mass is released, so the new mass is . The new upward acceleration is . * **Upward Force:** Buoyant force * **Downward Force:** New weight Applying the equation of motion for the new mass: --- ### **3. Algebraic Substitution** Substitute the value of from **Eq. 1** into **Eq. 2**: **Expand both sides:** **Cancel and simplify:** **Rearrange to group terms with :** --- ### **4. Final Result** Solving for : **Conclusion:** The mass that must be released is given by **Option (B)**.