$y = A{e^{ - \frac{{bt}}{{2m}}}}\sin (\omega 't + \phi )$
where the symbols have their usual meanings. If a $2\ kg$ mass $(m)$ is attached to a spring of force constant $(K)$ $1250\ N/m$ , the period of the oscillation is $\left( {\pi /12} \right)s$ . The damping constant $‘b’$ has the value. ..... $kg/s$
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| Column $I$ | Column $II$ |
| $(A)$ The energy of the system is increased |
$(p)$ $System:$ A capacitor, initially uncharged $Process:$ It is connected to a battery |
| $(B)$ Mechanical energy is provided to the system, which is converted into energy of random motion of its parts |
$(q)$ $System:$ A gas in an adiabatic container fitted with an adiabatic piston $Process:$ The gas is compressed by pushing the piston |
| $(C)$ Internal energy of the system is converted into its mechanical energy |
$(r)$ $System:$ A gas in a rigid container $Process:$ The gas gets cooled due to colder atmosphere surrounding it |
| $(D)$ Mass of the system is decreased |
$(s)$ $System:$ A heavy nucleus, initially at rest $Process:$ The nucleus fissions into two fragments of nearly equal masses and some neutrons are emitted |
|
$(t)$ $System:$ A resistive wire loop $Process:$ The loop is placed in a time varying magnetic field perpendicular to its plane |
