Energy(Work,Power,Energy)

Note :

1.For same momentum \(K.E\,\, \propto \,\,\frac{1}{m}\)
Kinetic energy varies inversely as the mass.
2. If two bodies have same momentum, ratio of their kinetic energy is 
\(\frac{{K.{E_1}}}{{K.{E_2}}}\,\, = \,\,\frac{{{m_2}}}{{{m_1}}}\)  \(\left[ {E\,\, \propto \,\,\frac{1}{m}} \right]\)                           
3.If two bodies have same kinetic energy, ratio of their momenta is \(\frac{{{P_1}}}{{{P_2}}}\,\, = \,\,\sqrt {\frac{{{m_1}}}{{{m_2}}}} \)
4.If the momentum of a body is increased to x times, its kinetic energy increases to x² times. 
5.If the kinetic energy of a body is increased to x times, its momentum increases to \(\sqrt{x}\) times.