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A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is 3.4 × 10⁵ J/kg and g = 10 N/kg]

1. 34 cm
2. 544 km
3. 136 km
4. 68 km

Correct answer: 136 km

Solution

The potential energy lost by the ice is mgh, and only one-quarter of this energy is absorbed as heat to melt the ice. Using the relation (1/4)mgh = mL, where L is the latent heat of ice, we solve for h: h = 4L/g. Substituting L = 3.4 × 10⁵ J/kg and g = 10 N/kg, we get h = 4 × (3.4 × 10⁵) / 10 = 1.36 × 10⁵ m = 136 km.

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