A small block slides down from the top of hemisphere of radius \(R=3\, {m}\) as shown in the figure. The height \('h'\) at which the block will lose contact with the surface of the sphere is \(.............  \;\;m\). (Assume there is no friction between the block and the hemisphere)

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \(2 \mathrm{~km} / \mathrm{s}\), the root mean square velocity of oxygen at the same condition in \(\mathrm{km} / \mathrm{s}\) is _______.

A shell is fired from a fixed artillery gun with an initial speed \(u\) such that it hits the target on the ground at a distance \(R\) from it. If \(t_1\) and \(t_2\) are the values of the time taken by it to hit the target in two possible ways, the product \(t_1t_2\) is

Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom ?

In a double -slit experiment, green light \(\left( {5303\,\mathop A\limits^o } \right)\) falls on a double slit having a separation of \(19.44\,\mu m\) and a width of \(4.05\,\mu m\). The number of bright fringes between the first and the second diffraction minima is

A circular hole of radius \(\left(\frac{ a }{2}\right)\) is cut out of a circular disc of radius \('a'\) as shown in figure. The centroid of the remaining circular portion with respect to point \('O'\) will be :

What is the conductivity of a semiconductor sample having electron concentration of \(5 \times 10^{18}\, m^{-3}\), hole concentration of \(5 \times  10^{19}\, m^{-3}\), electron mobility of \(2 .0\, m^2\, v^{-1}\, s^{-1}\) and hole mobility of \(0.01\, m^2\, v^{ -1}\, s^{-1}\) ?........\({\left( {\Omega  - m} \right)^{ - 1}}\) (Take charge of electron as \(1.6 \times 10^{-19}\, C\))

An effective power of a combination of \(5\) identical convex lenses which are kept in contact along the principal axis is \(25 \mathrm{D}\). Focal length of each of the convex lens is _______.

If the percentage errors in measuring the length and the diameter of a wire are \(0.1 \%\) each. The percentage error in measuring its resistance will be _______.

Consider the sound wave travelling in ideal gases of \(\mathrm{He}, \mathrm{CH}_4\), and \(\mathrm{CO}_2\). All the gases have the same ratio \(\frac{P}{\rho}\), where \(P\) is the pressure and \(\rho\) is the density. The ratio of the speed of sound through the gases \(\mathrm{v}_{\mathrm{He}}: \mathrm{v}_{\mathrm{CH}_4}: \mathrm{v}_{\mathrm{CO}_2}\) is given by