Define surface energy of the liquid. Obtain the relation between the surface energy and surface tension.
Surface energy is the energy needed to increase the surface area of a liquid by one unit area. It is associated with the force acting at the liquid's surface that resists expansion. Surface tension, which is the force per unit length acting along the surface, is directly related to surface energy. The relationship between surface energy \( E \) and surface tension \( T \) is expressed as: \[ E = T \cdot L \] where \( L \) is the length of the line along the surface.
Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the z direction. When filled with a liquid of surface tension \(S\) and density \( \rho \), the liquid surface makes angle \( \theta_0 \) (\( \theta_0 < < 1 \)) with the x-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is: (take \(g\) as the acceleration due to gravity)
Derive an expression for maximum speed of a vehicle moving along a horizontal circular track.
Predict the type of cubic lattice of a solid element having edge length of 400 pm and density of 6.25 g/ml.
(Atomic mass of element = 60)