JEE (Advanced) 2008 Paper-2
A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $$\overrightarrow{V_0} = V_0\hat{i}$$. The coefficient of friction is $$\mu$$.
For the following questions answer them individually
Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.
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An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.
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Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
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Cellulose upon acetylation with excess acetic anhydride/ $$H_2SO_4$$ (catalytic) gives cellulose triacetate whose structure is
In the following reaction sequence, the correct structures of E, F and G areÂ
(* implies $$^{13}C$$ labelled carbon)
Both $$[Ni(CO)_4]$$ and $$[Ni(CN)_4]^{2-}$$ are diamagnetic. The hybridisations of nickel in these complexes, respectively, are
