A pumpkin weighs 7.5 N. On sub- merging it completely in water, \(\frac{3}{4}\)L 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?

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  1. 10 kg/m3
  2. 100 kg/m3
  3. 1000 kg/m3
  4. 10000 kg/m3

Answer (Detailed Solution Below)

Option 3 : 1000 kg/m3
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Detailed Solution

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CONCEPT:

Density

  • Density is defined as mass per unit volume.
  • The formula to calculate density is:

    Density (ρ) = Mass / Volume

EXPLANATION:

  • In the given problem:
    • The weight of the pumpkin (W) = 7.5 N
    • The volume of water displaced (V) = 3/4 L = 0.75 L = 0.75 × 10-3 m3
    • The acceleration due to gravity (g) = 10 m/s2
  • First, calculate the mass (m) of the pumpkin:
    • Weight (W) = Mass (m) × Gravity (g)
    • m = W / g
    • m = 7.5 N / 10 m/s2
    • m = 0.75 kg
  • Next, calculate the density (ρ) of the pumpkin:
    • Density (ρ) = Mass (m) / Volume (V)
    • ρ = 0.75 kg / 0.75 × 10-3 m3
    • ρ = 0.75 kg / 0.00075 m3
    • ρ = 1000 kg/m3

Therefore, the correct value of the density of the pumpkin is 1000 kg/m3.

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