A piece of ice falls from a height `h` so that it melts completely. Only one-quarter of the heat produced is absobed 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 xx 10^(5) J//kg` and `g = 10 N//kg`]

Options

A. 136km
B. 68km
C. 34km
D. 544km

Answer

A

Explanation

Gravitational potential energy of a piece of ice at a height (h) = mgh
Heat absorbed by the ice to melt completely `Delta Q= (1)/(4) mgh`
..(i)
Also, `Delta Q= mL` …(ii)
From eqn (i) and (ii), `mL = (1)/(4) mgh or, h= (4L)/(g)`
Here `L= 3.4 xx 10^(5) J kg^(-1), g= 10 N kg^(-1)`
`:. h= (4 xx 3.4 xx 10^(5))/(10) = 4 xx 34 xx 10^(3) = 136 km`