Properties of Bulk Matter — Prelims Questions

A steel wire of length $L$, area of cross-section $A$, and Young's modulus $Y$ is stretched by a force $F$. The increase in its length is $\Delta L$. What is the elastic potential energy stored in the wire?

Water flows through a horizontal pipe whose one end is open to the atmosphere. The diameter of the pipe at one point is $4,\text{cm}$ and the velocity of water is $2,\text{m/s}$. At another point, the diameter is $2,\text{cm}$. What is the pressure difference between these two points? (Density of water $\rho = 1000,\text{kg/m}^3$)

A small spherical ball of radius $r$ and density $\rho$ is dropped in a viscous liquid of density $\sigma$ and coefficient of viscosity $\eta$. What is the terminal velocity of the ball?

A liquid drop of radius $R$ breaks into 64 smaller drops of equal radius. If the surface tension of the liquid is $T$, what is the change in surface energy?

A metal rod of length $2,\text{m}$ has a coefficient of linear expansion $2 \times 10^{-5},\text{/}^\circ C$. If its temperature is increased by $50^\circ C$, what is the percentage increase in its length?

An object floats in water with $1/3$ of its volume submerged. When it is placed in an oil, it floats with $1/4$ of its volume submerged. What is the density of the oil? (Density of water = $1000,\text{kg/m}^3$)

Which of the following statements is INCORRECT regarding the thermal conductivity of materials?