A block of ice with mass $m$ falls into a lake. After impact, a mass of ice $m/5$ melts. Both the block of ice and the lake have a temperature of $^o C$. If $L$ represents the heat of fusion, the minimum distance the ice fell before striking the surface is

A $20 \,g$ bullet whose specific heat is $5000 \,J kg ^{\circ} C$ and moving at $2000 \,m / s$ plunges into a $1.0 \,kg$ block of wax whose specific heat is $3000 \,J kg ^{\circ} C$. Both bullet and wax are at $25^{\circ} C$ and assume that $(i)$ the bullet comes to rest in the wax and $(ii)$ all its kinetic energy goes into heating the wax. Thermal temperature of the wax $\left(\right.$ in $\left.^{\circ} C \right)$ is close to

Morning breakfast gives $5000 \,cal$ to a $60 \,kg$ person. The efficiency of person is $30 \%$. The height upto which the person can climb up by using energy obtained from breakfast is ……… $m$

Equal masses of three liquids $A, B$ and $C$ have temperatures $10\,^oC$, $25\,^oC$ and $40\,^oC$ respectively. If $A$ and $B$ are mixed, the mixture has a temperature of $15\,^oC$. If $B$ and $C$ are mixed then mixture has temperature of $30\,^oC$. If $A$ and $C$ are mixed, the mixture will have a temperature of …….. $^oC$

$300 \,gm$ of water at $25^{\circ} C$ is added to $100 \,gm$ of ice at $0^{\circ} C$. The final temperature of the mixture is ……….. $^{\circ} C$