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Four pedagogic exercises

This article describes four innovative pedagogical exercises: (i) The expression for relation between cross sections in the laboratory and the centre of mass systems provided in text books assumes zero or low Q values which needs to be corrected for the most general case when Q value of the reaction is not negligible compared to the masses of interacting nuclei. The general expression derived here can be used for elastic and inelastic cases involving zero, low or even very high Q values. (ii) The equation of oscillatory motion of a massive surface put horizontally on two wheels rotating with equal and opposite angular velocities is established. The time period of oscillation is related to the coefficient of dynamic friction between the surface and the wheels which facilitates the measurement of the coefficient of dynamic friction. (iii) The equation of motion of a fixed torque mass shedding vehicle moving against friction and its velocity at any instant of time are derived. This example is equivalent to motion of a mass shedding rocket moving by applying fixed force against atmospheric friction. (iv) The equation of the path of a missile directed at every instant of time towards a rectilinearly moving target and time taken to hit the target are derived. It provides equation of path for asteroid and comet destructing missiles as conceptualized by NASA projects.