Question

A $30g$ of ice that is at a temperature $0^{\circ }C$ falls $6$ meters from the eaves of a house to the ground below. If $5$% of the kinetic energy that the ice possesses when it strikes the ground converts into heat, Identify the correct statement? (Note: $H_{f}water0.335J/g)$

• A. The ice would become colder during the fall; therefore, no ice would melt
• B. This would not happen because it would break the law of conservation of mass
• C. Less than $.3g$ of the ice would melt
• D. The frictional work done to stop the icicle's fall would use up all the energy and leave none for anything else
• E. The icicle would shatter and the energy would convert into momentum

Answer 1

The correct option is C Less than $.3g$ of the ice would melt

Given : $u=0m/s$ ; $h=6$ m; $m=30g=0.03kg$; $H_f=0.335J/g$

Kinetic energy of the ice when it strikes the ground is equal to the potential energy of the ice at a height of 6 m.

$\therefore$ $K.E=mgh=0.03\times 10\times 6=1.8$ $J$

Amount of kinetic energy converted into heat $Q=0.05\times 1.8=0.09$ $J$

Let the mass of ice melted due to energy converted into heat be $m^{\prime }$.

$\therefore$ $Q=m^{\prime }{H}_f$

OR $0.09=m^{\prime }\times 0.335$

$⟹m^{\prime }=0.27g$

Thus option C is correct.