Write down the dimensions of density, kinetic energy and power.
A sphere of radius \(r\) is moved at constant velocity \(v\) through a fluid.
In a viscous fluid, the power required is \(6 \pi \eta r v ^ { 2 }\), where \(\eta\) is the viscosity of the fluid.
Find the dimensions of viscosity.
In a non-viscous fluid, the power required is \(k \rho ^ { \alpha } r ^ { \beta } v ^ { \gamma }\), where \(\rho\) is the density of the fluid and \(k\) is a dimensionless constant.
Use dimensional analysis to find \(\alpha , \beta\) and \(\gamma\).
A rock of mass 5.5 kg is connected to a fixed point O by a light elastic rope with natural length 1.2 m . The rock is released from rest in a position 2 m vertically below O , and it next comes to instantaneous rest when it is 1.5 m vertically above O .
Find the stiffness of the rope.