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$A$ solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom?

The diagram shows a force-extension graph for a rubber band. Consider the following statements:
$(I)$ It will be easier to compress this rubber than expand it.
$(II)$ Rubber does not return to its original length after it is stretched.
$(III)$ The rubber band will get heated if it is stretched and released.
Which of these can be deduced from the graph?

An infinitely long rod lies along the axis of a concave mirror of focal length $f$. The near end of the rod is at a distance $u > f$ from the mirror. Its image will have a length:

Which set of compounds in the following pair of ionic compounds has the higher lattice energy?
$(i) \, KCl$ or $MgO$ $(ii) \, LiF$ or $LiBr$ $(iii) \, Mg_3N_2$ or $NaCl$

When a certain conductivity cell was filled with $0.1 \ M$ $KCl$,it had a resistance of $85 \ \Omega$ at $25 \ ^oC$. When the same cell was filled with an aqueous solution of $0.052 \ M$ unknown electrolyte,the resistance was $96 \ \Omega$. Calculate the molar conductivity of the unknown electrolyte at this concentration ............ $\Omega ^{-1} cm ^{2} mol ^{-1}$ (Given : Specific conductivity of $0.1 \ M$ $KCl = 1.29 \times 10^{-2} \ \Omega ^{-1} cm ^{-1}$)

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