The bob of a simple pendulum of mass $m$ and total energy $E$ will have maximum linear momentum equal to

The time period of a simple pendulum is $2 \, sec$. If its length is increased $4$ times,then its period becomes ..... $\sec$.

The bob of a swinging seconds pendulum (one whose time period is $2 \,s$) has a small speed $v_{0}$ at its lowest point. Its height from this lowest point $2.25 \,s$ after passing through it is given by

Two simple pendulums of length $0.5\, m$ and $2.0\, m$ respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed .... oscillations.

In the following table, the relation of the graph in column-$I$ and the shape of the graph in column-$II$ is shown. Match them appropriately.

Column-$I$	Column-$II$
$(a)$ $T^2 \to l$	$(i)$ Linear
$(b)$ $T^2 \to g$	$(ii)$ Parabolic
$(c)$ $T \to l$	$(iii)$ Hyperbolic

$A$ cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side $a$ is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is: