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Q.

A cube (side=10 cm) of density $0.5 g / c m^{3}$ is placed in a vessel of base area $20 c m \times 20 c m$ . A liquid of density $1.0 g / c m^{3}$ is gradually filled in the vessel at a constant rate $Q = 50 c m^{3} / s .$
The cube will leave contact with the vessel after time $t =_______s .$

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answer is 30.

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Detailed Solution

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$∴ (10 \times 10 \times 10) \times 0.5 \times g = 10 \times 10 \times x \times 1.0 \times g$

$∴ x = 5 cm$

Now, $Q \times t = (20 \times 20 - 10 \times 10) \times x$

$∴ t = \frac{300 \times 5}{50} = 30 s$

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A cube (side=10 cm) of density 0.5g/cm3 is placed in a vessel of base area 20cm×20cm. A liquid of density 1.0g/cm3 is gradually filled in the vessel at a constant rate Q = 50 cm3/s.The cube will leave contact with the vessel after time t=_______s.