Physics · Thermal Properties Of Matter · NEET
The energy going in is mgh (potential energy) and the energy needed to melt is mL (latent heat). Both sides carry the same mass m, so when you write f x mgh = mL and cancel m, you get h = L / (f x g). The height needed to melt does not depend on how heavy the ice is. A tiny ice cube and a huge block need the same drop height. This is why exam questions never give you the mass - it is not needed.
Only if the ice starts below 0 C. In the standard NEET problem the ice is already at its melting point (0 C), so no heat is spent raising temperature - all the absorbed heat goes straight into melting. Then you use only mL. If a question says the ice starts at, say, -10 C, you must first add m c delta T to warm it to 0 C, then add mL to melt it, so total heat = m c delta T + m L.
When ice hits the ground the kinetic energy becomes heat, but that heat spreads into the ground, the air, and the ice. If only a fraction f is absorbed by the ice, then only f x (mgh) melts it. So f x mgh = mL. With f = 1/4 the equation becomes (1/4) mgh = mL, giving h = 4L/g. A smaller fraction means a larger height is needed, because less of the fall's energy actually reaches the ice.
Latent heat of ice is huge: L = 3.4 x 10^5 J per kg. Gravity only gives g = 10 J per kg for every metre of drop. So to supply 3.4 x 10^5 J per kg you need a drop of L/g = 3.4 x 10^4 m even at full efficiency. With only 1/4 absorbed, h = 4L/g = 1.36 x 10^5 m = 136 km. The numbers are unphysical on purpose - the exam is testing the energy balance, not real weather.
Ignore air friction in these problems. The ice stays at 0 C during melting because a phase change happens at constant temperature. The falling energy is not warming it above 0 C - it is being spent breaking the solid bonds to turn ice into water at the same 0 C. Temperature stays fixed while state changes.
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 the gravitational energy is converted into heat. The value of h is: (latent heat of ice = 3.4 x 10^5 J/kg, g = 10 N/kg)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Set the useful heat equal to the melting heat: f x mgh = mL, where f is the fraction of heat absorbed by the ice, g is gravity, h is the drop height, and L is the latent heat of fusion. Solving gives h = L / (f x g).
NCERT gives Lf = 3.33 x 10^5 J/kg. Exam questions often round it, for example the NEET 2016 question uses 3.4 x 10^5 J/kg. Always use the value stated in the question.
Because the ice is at its melting point (0 C) and undergoes a phase change at constant temperature. No heat is spent on m c delta T, so only the latent heat term mL is used and temperature drops out of the formula.
Then add a warming step first: total heat needed = m c delta T (to reach 0 C) + m L (to melt). The fall energy must supply both, so f x mgh = m c delta T + m L.
For NEET, assume no air resistance unless stated. All lost potential energy mgh becomes heat, and the given fraction f decides how much of that heat actually goes into the ice.
