Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
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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