The time period of a second's pendulum is $2\, s$. The spherical bob,which is empty from inside,has a mass of $50\, g$. This is now replaced by another solid bob of the same radius but having a mass of $100\, g$. The new time period will be .... $s$.

Which one of the following is not an iso-electronic pair?

The equation $\sqrt{3} \sin x + \cos x = 4$ has

If the volume of a parallelepiped with coterminous edges $4 \hat{i} + 5 \hat{j} + \hat{k}$,$-\hat{j} + \hat{k}$,and $3 \hat{i} + 9 \hat{j} + p \hat{k}$ is $34$ cubic units,then $p$ is equal to:

The coefficients of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$,respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$,the coefficient of linear expansion of the vessel $B$ is

$A$ $U$-tube has a left limb with a cross-sectional area that is one-quarter of the right limb. The tube contains mercury (density $13.6 \ g/cm^3$). The level of mercury in the narrow left limb is at a distance of $36 \ cm$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water (in $cm$)? (Density of water = $1 \ g/cm^3$)