If the displacement $y$ (in cm ) of a particle executing simple harmonic motion is given by the equation $y=5 \sin (3 \pi t)+5 \sqrt{3} \cos (3 \pi t)$, then the amplitude of the particle is

The angular frequency of a block of mass 0.1 kg oscillating with the help of a spring of force constant $2.5 \mathrm{~N}-\mathrm{m}^{-1}$ is

An infinite number of objects each 1 kg mass are placed on the $X$-axis on both sides of $x=0$ at $\pm 1 \mathrm{~m}$, $\pm 2 \mathrm{~m}, \pm 4 \mathrm{~m}, \pm 8 \mathrm{~m} \ldots \ldots$ and so on. The magnitude of the resultant gravitational potential (in SI units) at $x=0$ is

( $G=$ Universal gravitational constant)

As shown in the figure, a light uniform rod $P Q$ of length 150 cm is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of the two wires $A$ and $B$ are respectively $2: 3$ and $3: 2$. The position at which a weight should be suspended from the rod such that the elongations of the two wires become equal is