The value of coefficient of volume expansion of glycerin is $5 \times 10^{-4}k^{-1} .$ The fractional change in the density of glycerin for a rise of $40^o C$ in its temperature, is

A block of wood is floating on water at $0^{\circ} C$ with volume $V_0$ above water. When the temperature of water increases from $0$ to $10^{\circ} C$, the change in the volume of the block that is above water is best described schematically by the graph.

If in winter season the surface temperature of lake is $1^{\circ} C$, the temperature at the bottom of lake will be …………

A rod of length $20\, cm$ is made of metal. It expands by $0.075cm$ when its temperature is raised from $0°C$ to $100°C.$ Another rod of a different metal $B$ having the same length expands by $0.045 \,cm$ for the same change in temperature. $A$ third rod of the same length is composed of two parts, one of metal $A$ and the other of metal $B$. This rod expands by $0.060\, cm$ for the same change in temperature. The portion made of metal $A$ has the length …….. $cm$

A hole is drilled in a metal sheet. At $27^{\circ}\,C$, the diameter of hole is $5\,cm$. When the sheet is heated to $177^{\circ}\,C$, the change in the diameter of hole is $d \times$ $10^{-3}\,cm$. The value of $d$ will be $………..$ if coefficient of linear expansion of the metal is $1.6 \times$ $10^{-5} /{ }^{\circ}\,C$