A pumpkin weighs 7.5 N. On submerging it completely in water, 2L of water gets displaced. The acceleration due to gravity at the place where the pumpkin was weighed is 10 m/s2. Which one of the following is the correct value of the density of the pumpkin ?

The density of an object is defined as its mass per unit volume (ρ = m/V). To find the density of the pumpkin, we follow these steps:

• Calculate Mass: Given the weight of the pumpkin is 7.5 N and the acceleration due to gravity (g) is 10 m/s², the mass (m) is calculated as:
  m = Weight / g = 7.5 / 10 = 0.75 kg.
• Identify Volume: According to Archimedes' principle, when an object is completely submerged, the volume of the displaced liquid equals the volume of the object. In the official UPSC NDA (II) 2024 paper, the volume of water displaced is 3/4 L (0.75 L).
• Calculate Density: Converting volume to cubic meters (1 L = 10⁻³ m³):
  V = 0.75 × 10⁻³ m³ = 0.00075 m³.
  ρ = 0.75 kg / 0.00075 m³ = 1000 kg/m³.

This calculation confirms that the density of the pumpkin is 1000 kg/m³, aligning with Option C.