The mass of proton, neutron and helium nucleus are respectively \(1.0073\,u , 1.0087\,u\) and \(4.0015\,u\). The binding energy of helium nucleus is \(.........\,MeV\)

The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be \(............\,L\)

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension \(70 \mathrm{dyn} / \mathrm{cm}\) and glass water contact angle \(\simeq 0^{\circ}\)) with \(30^{\circ}\) inclined with vertical. The length of water risen in the capillary is ________ cm.
\(\left(\right.\) Take \(\left.\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)\)

The maximum percentage error in the measurment of density of a wire is [Given, mass of wire \(=(0.60 \pm 0.003) \mathrm{g}\)
radius of wire \(=(0.50 \pm 0.01) \mathrm{cm}\)
length of wire \(=(10.00 \pm 0.05) \mathrm{cm}]\)

Select the correct statement from the following

Figure shows elliptical path \(abcd\) of a planet around the sun \(S\) such that the area of triangle \(csa\) is \(\frac {1}{4}\) the area of the ellipse. (See figure) With \(db\)  as the semimajor axis, and  \(ca\) as the semiminor axis. If \(t_1\)  is the time taken for planet to go over path \(abc\) and \(t_2\) for path taken over \(cda\) then

A point light source emits E.M. waves in free space. A detector, placed at a distance of \(L\) m, measures the intensity as \(I_o\). The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as \(45°\). The measured intensity at new location will be _______.

A small mirror of mass \(m\) is suspended by a massless thread of length \(l\). Then the small angle through which the thread will be deflected when a short pulse of laser of energy \(E\) falls normal on the mirror ( \(\mathrm{c}=\) speed of light in vacuum and \(\mathrm{g}=\) acceleration due to gravity)

10 mole of oxygen is heated at constant volume from \(30^{\circ} C\) to \(40^{\circ} C\). The change in the internal energy of the gas is _________ cal. (The molecular specific heat of oxygen at constant pressure, \(C _{ p }=7 cal . / mol ^{\circ} C\) and \(\left.R =2 cal . / mol ^{\circ} C .\right)\)

Due to cold weather a \(1\, {m}\) water pipe of cross-sectional area \(1\, {cm}^{2}\) is filled with ice at \(-10^{\circ} {C}\). Resistive heating is used to melt the ice. Current of \(0.5\, {A}\) is passed through \(4\, {k} \Omega\) resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In \({s}\)) (Given latent heat of fusion for water/ice \(=3.33 \times 10^{5}\, {J} {kg}^{-1}\), specific heat of ice \(=2 \times 10^{3}\, {J}\) \({kg}^{-1}\) and density of ice \(=10^{3}\, {kg} / {m}^{3}\)

When two sound waves travel in the same direction in a medium, the displacements of a particle located at \('x'\) at time \('t'\) is given by \({y_1} = 0.05\,\cos \,\left( {0.50\,\pi x - 100\,\pi t} \right)\) \({y_2} = 0.05\,\cos \,\left( {0.46\,\pi x - 92\,\pi t} \right)\) then velocity is..... \(m/s\)

A beam of plane polarised light of large cross sectional area and uniform intensity of \(3.3 \,Wm ^{-2}\) falls normally on a polariser (cross sectional area \(3 \times 10^{-4}\, m ^{2}\) ) which rotates about its axis with an angular speed of \(31.4\, rad/s.\) The energy of light passing through the polariser per revolution, is close to ........ \( \times 10^{-4} \,J\)

A solid body of constant heat capacity \(1\ J/^o C\) is being heated by keeping it in contact with reservoirs in two ways : \((i)\) Sequentially keeping in contact with \(2\) reservoirs such that each reservoir supplies same amount of heat. \((ii)\) Sequentially keeping in contact with \(8\) reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature \(100^o C\) to final temperature \(200^o C\). Entropy change of the body in the two cases respectively is :