What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless?

$A$ $TV$ transmitting antenna is $128 \ m$ tall. If the receiving antenna is at the ground level,the maximum distance between them for satisfactory communication in line-of-sight mode is (radius of the earth $R_e = 6.4 \times 10^6 \ m$):

The gold numbers of $A$,$B$,$C$,and $D$ are $0.04$,$0.002$,$10$,and $25$ respectively. The protective power of $A$,$B$,$C$,and $D$ are in the order:

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

An electron accelerated through a potential difference $V$ enters a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2V$,the electron in the same magnetic field will experience a force:

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to produce caustic soda. When $CO_2$ is passed through a solution of $A$,it turns milky. What is the chemical formula of $A$?