$A$ wooden block, with a coin placed on its top, floats in water as shown in the figure. The distances $l$ and $h$ are shown. After some time, the coin falls into the water. Then:

In the reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $B$ was $1.5$ times that of $[A]$. At equilibrium,the concentrations of $A$ and $B$ became equal. The equilibrium constant $K_c$ for the reaction is:

Let $f$ be defined on $D = \mathbb{R} - \{-1, 1\}$ by $f(x) = \frac{|x|}{1-|x|}$,then

$A$ bomb is projected with $200 \, m/s$ at an angle $60^o$ with the horizontal. At the highest point,it explodes into three particles of equal masses. One goes vertically upward with a velocity of $100 \, m/s$,and the second particle goes vertically downward with the same velocity as the first. What is the velocity of the third particle?

$A$ particle of charge '$q$' and mass '$m$' moves in a circular orbit of radius '$r$' with angular speed '$\omega$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

Two strings $A$ and $B$ of lengths $L_A = 80 \ cm$ and $L_B = x \ cm$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency,the value of $x$ is: