Properties of Matter Questions

When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire becomes $(L+l)$. The elastic potential energy stored in the extended wire is:

A soap bubble, having radius of $1\text{mm}$, is blown from a detergent solution having a surface tension of $2.5\times 10^{-2}\text{N/m}$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of water in a container. Taking $g=10{\text{m/s}}^2$, density of water $=10^3{\text{kg/m}}^3$, the value of $Z_0$ is:

A small hole of area of cross-section $2{\text{mm}}^2$ is present near the bottom of a fully filled open tank of height $2\text{m}$. Taking $g=10{\text{m/s}}^2$, the rate of flow of water through the open hole would be nearly:

The stress-strain curves are drawn for two different materials $X$ and $Y$. It is observed that the ultimate strength point and the fracture point are close to each other for material $X$ but are far apart for material $Y$. We can say that the materials $X$ and $Y$ are likely to be (respectively):

In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are $15\text{cm}$ and $20\text{cm}$ respectively. The density of the oil is (${\rho }_{water}=1000{\text{kg/m}}^3$):

Two small spherical metal balls, having equal masses, are made from materials of densities ${\rho }_1$ and ${\rho }_2$ such that ${\rho }_1=8{\rho }_2$ and having radii of $r_1$ and $r_2$, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1{\rho }_2$. The ratio of their terminal velocities would be:

A deep rectangular pond of surface area $A$, containing water (density = $\rho$, specific heat capacity = $s$), is located in a region where the outside air temperature is at a steady value of $-26^{\circ }\text{C}$. The thickness of the ice layer in this pond at a certain instant is $x$. Taking the thermal conductivity of ice as $k$, and its specific latent heat of fusion as $L$, the rate of increase of the thickness of the ice layer, at this instant, would be given by:

An object kept in a large room having an air temperature of $25^{\circ }\text{C}$ takes $12\text{min}$ to cool from $80^{\circ }\text{C}$ to $70^{\circ }\text{C}$. The time taken to cool for the same object from $70^{\circ }\text{C}$ to $60^{\circ }\text{C}$ would be nearly: