$\begin{array}{l}
{I_0} = {I_{cm}} + m{d^2}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{7M{R^2}}}{2} + 6\left( {M \times {{\left( {2R} \right)}^2}} \right) = \frac{{55M{R^2}}}{2}
\end{array}$
Again, moment of inertia about point P,${I_P} = {I_0} + m{d^2}$
$ = \frac{{55M{R^2}}}{2} + 7M{\left( {3R} \right)^2} = \frac{{181}}{2}M{R^2}$
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The tensions $T_1$ and $T_2$ in the string are respectively
| Column $I$ | Column $II$ |
| $(A)$ The force exerted by $\mathrm{X}$ on $\mathrm{Y}$ has a magnitude $\mathrm{Mg}$. | $Image$ Block $Y$ of mass $M$ left on a fixed inclined plane $\mathrm{X}$, slides on it with a constant velocity. |
| $(B)$ The gravitational potential energy of $\mathrm{X}$ is continuously increasing. | $Image$ Two ring magnets $\mathrm{Y}$ and $\mathrm{Z}$, each of mass $M$, are kept in frictionless vertical plastic stand so that they repel each other. $Y$ rests on the base $X$ and $\mathrm{Z}$ hangs in air in equilibrium. $\mathrm{P}$ is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity. |
| $(C)$ Mechanical energy of the system $\mathrm{X}+\mathrm{Y}$ is continuously decreasing. | $Image$ A pulley $Y$ of mass $m_0$ is fixed to a table through a clamp $X$. A block of mass $M$ hangs from a string that goes over the pulley and is fixed at point $\mathrm{P}$ of the table. The whole system is kept in a lift that is going down with a constant velocity. |
| $(D)$ The torque of the weight of $\mathrm{Y}$ about point $\mathrm{P}$ is zero. | $Image$ A sphere $\mathrm{Y}$ of mass $M$ is put in a nonviscous liquid $\mathrm{X}$ kept in a container at rest. The sphere is released and it moves down in the liquid. |
| $Image$ A sphere $\mathrm{Y}$ of mass $M$ is falling with its terminal velocity in a viscous liquid $\mathrm{X}$ kept in a container. |
