$A$ lead bullet of mass $10 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of heat is absorbed by the bullet, the increase in its temperature is (Specific heat of lead $= 150 \ J/kg \cdot ^{\circ}C$) (in $^{\circ}C$)

The radiator of an engine is cooled by water because:

How much heat energy is gained when $5\, kg$ of water at $20^{\circ}C$ is brought to its boiling point? (Specific heat of water $= 4.2\, kJ\, kg^{-1} {^{\circ}C}^{-1}$)

The figure below shows the variation of specific heat capacity $(C)$ of a solid as a function of temperature $(T)$. The temperature is increased continuously from $0$ to $500 \ K$ at a constant rate. Ignoring any volume change,which of the following statement$(s)$ is (are) correct to a reasonable approximation?
$(A)$ The rate at which heat is absorbed in the range $0-100 \ K$ varies linearly with temperature $T$.
$(B)$ Heat absorbed in increasing the temperature from $0-100 \ K$ is less than the heat required for increasing the temperature from $400-500 \ K$.
$(C)$ There is no change in the rate of heat absorption in the range $400-500 \ K$.
$(D)$ The rate of heat absorption increases in the range $200-300 \ K$.

$A$ $10\, kW$ drilling machine is used to drill a bore in a small aluminium block of mass $8.0\, kg$. How much is the rise in temperature of the block in $2.5$ minutes,assuming $50\, \%$ of power is used up in heating the machine itself or lost to the surroundings? (Specific heat of aluminium $= 0.91\, J\, g^{-1}\, K^{-1}$)

Two spheres made of the same substance have diameters in the ratio $1:2$. Their thermal capacities are in the ratio of: