Question:
An object hangs from a spring balance. The balance shows 40 N when the object is in air, 30 N when the object is immersed in water, and 34 N when the object is immersed in another liquid. If the density of water is 1000 kg m\(^{-3}\), then the density of the liquid is
An object hangs from a spring balance. The balance shows 40 N when the object is in air, 30 N when the object is immersed in water, and 34 N when the object is immersed in another liquid. If the density of water is 1000 kg m\(^{-3}\), then the density of the liquid is
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Buoyant force is directly proportional to the density of the fluid for the same submerged volume.
Updated On: Jun 20, 2026
- 500 kg m\(^{-3}\)
- 800 kg m\(^{-3}\)
- 750 kg m\(^{-3}\)
- 600 kg m\(^{-3}\)
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The Correct Option is D
Solution and Explanation
Step 1: Understand the concept of buoyant force.
The apparent loss of weight in a fluid is equal to the buoyant force: \[ F_b = W_{\text{air}} - W_{\text{liquid}} \]
Step 2: Find buoyant force in water.
\[ F_{b,w} = 40 - 30 = 10 \, \text{N} \]
Step 3: Find buoyant force in unknown liquid.
\[ F_{b,l} = 40 - 34 = 6 \, \text{N} \]
Step 4: Use Archimedes’ principle.
Buoyant force is proportional to density of fluid: \[ \frac{F_{b,l}}{F_{b,w}} = \frac{\rho_l}{\rho_w} \]
Step 5: Substitute values.
\[ \frac{6}{10} = \frac{\rho_l}{1000} \] \[ \rho_l = \frac{6}{10} \times 1000 \] \[ \rho_l = 600 \, \text{kg m}^{-3} \]
Step 6: Final conclusion.
Thus, density of the liquid is: \[ \boxed{600 \, \text{kg m}^{-3}} \]
The apparent loss of weight in a fluid is equal to the buoyant force: \[ F_b = W_{\text{air}} - W_{\text{liquid}} \]
Step 2: Find buoyant force in water.
\[ F_{b,w} = 40 - 30 = 10 \, \text{N} \]
Step 3: Find buoyant force in unknown liquid.
\[ F_{b,l} = 40 - 34 = 6 \, \text{N} \]
Step 4: Use Archimedes’ principle.
Buoyant force is proportional to density of fluid: \[ \frac{F_{b,l}}{F_{b,w}} = \frac{\rho_l}{\rho_w} \]
Step 5: Substitute values.
\[ \frac{6}{10} = \frac{\rho_l}{1000} \] \[ \rho_l = \frac{6}{10} \times 1000 \] \[ \rho_l = 600 \, \text{kg m}^{-3} \]
Step 6: Final conclusion.
Thus, density of the liquid is: \[ \boxed{600 \, \text{kg m}^{-3}} \]
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