$A$ mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface,collides with a nearly weightless spring of force constant $k=50\, N/m$. The maximum compression of the spring would be ................. $m$.

How does the $pH$ of blood in arteries compare to that in veins?

Six wires each of cross-sectional area $A$ and length $l$ are combined as shown in the figure. The thermal conductivities of copper and iron are $K_1$ and $K_2$ respectively. The equivalent thermal resistance between points $A$ and $C$ is

Let $\vec{p}$ and $\vec{q}$ be the position vectors of points $P$ and $Q$ with respect to the origin $O$,and $|\vec{p}| = p$,$|\vec{q}| = q$. If points $R$ and $S$ divide the line segment $PQ$ internally and externally in the ratio $2:3$ respectively,and if $\vec{OR} \perp \vec{OS}$,then:

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2,$ respectively. If the maximum velocities during oscillations are equal,the ratio of amplitudes of $A$ and $B$ is

If $u=f(r)$,where $r^2=x^2+y^2$,then $\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right)$ is equal to