Properties of Matter

Two wires are made of the same material and have the same volume. However wire \(1\) has cross-sectional area \(A\) and wire \(2\) has cross-sectional area \(3A.\) If the length of wire \(1\) increases by \(\Delta x\) on applying force $$F,...

A spherical solid ball of volume \(V\) is made of a material of density \({\rho _1}\). It is falling through a liquid of density \({\rho _2}\left( {{\rho _2} < {\rho _1}} \right)\). Assume that the liquid applies a viscous force on the ball...

A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

A jar is filled with two non-mixing liquids \(1\) and \(2\) having densities \({\rho _1}\) and \({\rho _2}\) respectively. A solid ball, made of a material of density \({\rho _3}\), is dropped in the jar. It comes to equilibrium in the pos...

If the terminal speed of a sphere of gold (density \(= 19.5\,\,kg/{m^3}\)) is \(0.2\) \(m/s\) in a viscous liquid (density \(= 1.5\,\,kg/{m^3}\), find the terminal speed of a sphere of silver (density \(= 10.5\,\,kg/{m^3}\)) of the same ...

A wire elongates by \(l\) \(mm\) when a LOAD \(W\) is hanged from it. If the wire goes over a pulley and two weights \(W\) each are hung at the two ends, the elongation of the wire will be (in \(mm\))

If \(S\) is stress and \(Y\) is young's modulus of material of a wire, the energy stored in the wire per unit volume is

A \(20\) \(cm\) long capillary tube is dipped in water. The water rises up to \(8\) \(cm.\) If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

A wire fixed at the upper end stretches by length \(l\) by applying a force \(F.\) The work done in stretching is

If two soap bubbles of different radii are connected by a tube

Spherical balls of radius \(R\) are falling in a viscous fluid of viscosity \(\eta\) with a velocity \(v.\) The retarding viscous force acting on the spherical ball is

According to Newton's law of cooling, the rate of cooling of a body is proportional to \({\left( {\Delta \theta } \right)^n},\) where \({\Delta \theta }\) is the difference of the temperature of the body and the surrounding, and \(n\) is e...

A cylinder of height \(20\) \(m\) is completely filled with water. The velocity of efflux of water (in \(m{s^{ - 1}}\)) through a small hole on the side wall of the cylinder near its bottom is