A body falling under gravity covers two points \(A\) and \(B\) separated by \(80 \mathrm{~m}\) in \(2 \mathrm{~s}\). The distance of upper point A from the starting point is________ \(\mathrm{m}\) (use \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

A body of mass 4 kg is placed on a plane at a point P having coordinate \((3,4) \mathrm{m}\). Under the action of force \(\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}\), it moves to a new point Q having coordinates \((6,10) \mathrm{m}\) in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is \(T\), density of liquid is \(\rho\) and \(L\) is its latent heat of vaporization

A thin prism \(P_1\) with an angle \(6^{\circ}\) and made of glass of refractive index \(1.54\) is combined with another prism \(P _2\) made from glass of refractive index \(1.72\) to produce dispersion without average deviation. The angle of prism \(P_2\) is \(........{}^{\circ}\)

Two parallel plate capacitors of capacity \(C\) and \(3\,C\) are connected in parallel combination and charged to a potential difference \(18\,V\). The battery is then disconnected and the space between the plates of the capacitor of capacity \(C\) is completely filled with a material of dielectric constant \(9\). The final potential difference across the combination of capacitors will be \(V\)

An amount of ice of mass \(10^{-3} \mathrm{~kg}\) and temperature \(-10^{\circ} \mathrm{C}\) is transformed to vapour of temperature \(110^{\circ} \mathrm{C}\) by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice \(=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\), specific heat of water \(=4180 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\), specific heat of steam \(=1920 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\), Latent heat of ice \(=3.35 \times 10^5 \mathrm{Jkg}^{-1}\) and Latent heat of steam \(=2.25 \times 10^6\) \(\mathrm{Jkg}^{-1}\) )

An antenna is placed in a dielectric medium of dielectric constant \(6.25\). If the maximum size of that antenna is \(5.0\, mm\). it can radiate a signal of minimum frequency of \(GHz .\) (Given \(\mu_{ r }=1\) for dielectric medium)

When a rubber-band is stretched by a distance \(x\), it exerts restoring force of magnitude  \(F=ax+bx^2\) where \(a\) and \(b\) areconstants. The work done in stretching the unstretched rubber-band by \(L\) is

Consider two containers \(A\) and \(B\) containing monoatomic gases at the same Pressure \((P)\), Volume \((V)\) and Temperature \((T)\). The gas in \(A\) is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas \(B\) is compressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in \(B\) to that of gas in \(A\) is ...........