$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ moving with velocity $v$ strikes the rod at one end perpendicular to the rod. After the collision,the particle comes to rest. The velocity of the centre of mass of the rod after the collision is:

Which of the following statements are correct for alkali metal compounds?
$(i)$ Superoxides are paramagnetic in nature.
$(ii)$ The basic strengths of hydroxides increase down the group.
$(iii)$ The conductivity of chlorides in their aqueous solutions decreases down the group.
$(iv)$ The basic nature of carbonates in aqueous solutions is due to cationic hydrolysis.

What is the hybridization state of the central atom in the conjugate base of $NH_4^{+}$ ion?

Which one of the following has the smallest diameter?

The system shown in the figure is released from rest. The pulley and spring are massless,and friction is absent everywhere. The speed of the $5\, kg$ block when the $2\, kg$ block leaves contact with the ground is: (Take the force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2$)

Intercalary meristem results in