$20 \text{ mL}$ of $0.1 \text{ M}$ acetic acid is mixed with $50 \text{ mL}$ of potassium acetate. $K_a$ of acetic acid $= 1.8 \times 10^{-5}$ at $27^\circ \text{C}$. Calculate the concentration of potassium acetate if the $pH$ of the mixture is $4.8$. (in $\text{ M}$)

There is a uniform electric field of strength $10^3 \ Vm^{-1}$ along the $Y$-axis. $A$ body of mass $1 \ g$ and charge $10^{-6} \ C$ is projected into the field from the origin along the positive $X$-axis with a velocity of $10 \ ms^{-1}$. Its speed in $ms^{-1}$ after $10 \ s$ is (Neglect gravitation).

$A$ solid sphere and a disc of same mass $M$ and radius $R$ are kept such that their curved surfaces are in contact and their centers lie along the same horizontal line. The moment of inertia of the two-body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

In a permanent magnet at room temperature,

An infinitely long straight conductor is bent into the shape as shown below. It carries a current of $I$ ampere and the radius of the circular loop is $R$ metre. Then,the magnitude of magnetic induction at the centre of the circular loop is

In an optical fibre,the core and cladding are made with materials of refractive indices $1.5$ and $1.414$ respectively. To observe total internal reflection,what will be the range of the incident angle with the axis of the optical fibre?