A straight conducting bar of mass $m$ and length $l$ is suspended horizontally with two non-conducting springs of stiffness $k$ as shown in the figure. The capacitor is initially charged to the potential difference $U$. At time $t=0$ , the switch $S$ is closed and the capacitor discharges. The bar starts oscillating in the vertical plane.


Find the amplitude of these oscillations: (Assume the time of discharge of the capacitor is much smaller than the period $T$ of the mechanical oscillation of the bar)

A mass of  $0.5 \mathrm{kg}$ moving with a speed of $1.5 \mathrm{m} {\mathrm{s}}^{-1}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $\mathrm{k}=50 \mathrm{N} {\mathrm{m}}^{-1}$. The maximum compression of the spring would be

The graphs below show the magnitude of the force on a particle as it moves along the positive $X$-axis from the origin to $X=X_1$. The force is parallel to the $X$-axis and conservative. The maximum magnitude $F_1$ has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

A large block of wood of mass $M=5.99 \mathrm{kg}$ is hanging from two long massless cords. A bullet of mass $m=10 \mathrm{g}$ is fired into the block and gets embedded in it. The (block $+$ bullet) then swing upwards, their center of mass rising a vertical distance $h=9.8 \mathrm{cm}$ before the (block $+$ bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before the collision is: (Take $g=9.8{ \mathrm{m} \mathrm{s}}^{-2}$)