The height of any point \(P\) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \(P\) will be : (Given \(g=\) acceleration due to gravity at the surface of earth)

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is \(5\, cm\) and the angular speed of rotation is  \(\omega\; rad \,s^{-1}\). The difference in the height, \(h(\) in \(cm )\) of liquid at the centre of vessel and at the side will be

When an object is kept at a distance of \(30\, cm\) from a concave mirror, the image is formed at a distance of \(10\, cm\) from the mirror. If the object is moved with a speed of \(9\, cms ^{-1}\), the speed (in \(cms ^{-1}\) ) with which image moves at that instant is\(....m/s\)

A bakelite beaker has volume capacity of \(500\, cc\) at \(30^{\circ} C\). When it is partially filled with \(V _{ m }\) volume (at \(30^{\circ}\) ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} C ^{-1}\) and \(\gamma_{(\text {mercury })}=1.5 \times 10^{-4}{ }^{\circ} C ^{-1},\) where \(\gamma\) is the coefficient of volume expansion, then \(V _{ m }(\)in \(cc )\) is close to

An alpha-particle of mass \(m\) suffers \(1-\) dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, \(64\%\) of its initial kinetic energy. The mass of the nucleus is .......... \(\mathrm{m}\)

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \(\frac{C_p}{C_v}\) for the gas is:

A cricket ball of mass \(0.15\, kg\) is thrown vertically up by a bowling machine so that it rises to a maximum height of \(20 \;m\) after leaving the machine. If the part pushing the ball applies a constant force \(F\) on the ball and moves horizontally a distance of \(0.2\, m\) while launching the ball, the value of \(F(\) in \(N)\) is  \(\left(g=10\, m s^{-2}\right)\)

A water spray gun is attached to a hose of cross sectional area \(30\) cm\(^2\). The gun comprises of \(10\) perforations each of cross sectional area \(15\) mm\(^2\). If the water flows in the hose with the speed of \(50\) cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

A fish rising vertically upward with a uniform velocity of \(8\,ms ^{-1}\), observes that a bird is diving vertically downward towards the fish with the velocity of \(12\,ms ^{-1}\). If the refractive index of water is \(\frac{4}{3}\), then the actual velocity of the diving bird to pick the fish, will be \(.......\,ms ^{-1}\).

A parallel beam of light of wavelength \(900\,nm\) and intensity \(100\,Wm ^{-2}\) is incident on a surface perpendicular to the beam. Tire number of photons crossing \(1\,cm ^{2}\) area perpendicular to the beam in one second is :

A charge \(Q\) is placed at a distance \(a/2\) above the centre of the square surface of edge \(a\) as shown in the figure. The electric flux through the square surface is

A uniform thin rod \(AB\) of length \(L\) has linear mass density \(\mu \left( x \right) = a + \frac{{bx}}{L}\) , where \(x\) is measured from \(A\). If the \(CM\) of the rod lies at a distance of \(\left( {\frac{7}{12}} \right)L\) from \(A\), then \(a\) and \(b\) are related as

An \(AC\) circuit has \(R =100 \Omega, C =2\, \mu F\) and \(L =80\, mH ,\) connected in series. The quality factor of the circuit is\(.......\)