The figure shows the vertical section of a frictionless surface. $A$ block of mass $2\, kg$ is released from position $A$. Its kinetic energy $(KE)$ as it reaches position $C$ is ................ $J$.

In a system of two particles of masses $m_{1}$ and $m_{2}$,the second particle is moved by a distance $d$ towards the centre of mass. To keep the centre of mass unchanged,the first particle will have to be moved by a distance:

Two ideal slits $S_1$ and $S_2$ are at a distance $d$ apart and are illuminated by light of wavelength $\lambda$ passing through an ideal source slit $S$ placed on the line through $S_2$ as shown. The distance between the plane of the slits and the source slit is $D$. $A$ screen is held at a distance $D$ from the plane of the slits. The minimum value of $d$ for which there is darkness at $O$ is

$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is:

The $pK_a$ of a weak acid is $4.8$. What should be the ratio of $[Acid]/[Salt]$ of a buffer if $pH = 5.8$ is required?

$A$ mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass at rest. After the collision,the $1^{st}$ mass moves with a velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{nd}$ mass after the collision.