A porter lifts a heavy suitcase of mass \(80\, {kg}\) and at the destination lowers it down by a distance of \(80\, {cm}\) with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. (take \(g=9.8\, {ms}^{-2}\) ) (In \({J}\))

Two satellites \(A\) and \(B\) move round the earth in the same orbit. The mass of \(A\) is twice the mass of \(B\). The quantity which is same for the two satellites will be :

A uniform solid cylindrical roller of mass \('m'\) is being pulled on a horizontal surface with force \(F\) parallel to the surface and applied at its centre. If the acceleration of the cylinder is \('a'\) and it is rolling without slipping then the value of \('F'\) is 

The entropy of any system is given by \({S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]\) Where \(\alpha\) and \(\beta\) are the constants. \(\mu, J, K\) and \(R\) are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant repectively. [Take \({S}=\frac{{dQ}}{{T}}\) ] Choose the incorrect option from the following:

Suppose two planets (spherical in shape) of radii \({R}\) and \(2 {R}\), but mass \({M}\) and \(9\, {M}\) respectively have a centre to centre separation \(8\, {R}\) as shown in the figure. A satellite of mass \('{m}'\) is projected from the surface of the planet of mass \('M'\) directly towards the centre of the second planet. The minimum speed \('v'\) required for the satellite to reach the surface of the second planets is \(\sqrt{\frac{a}{7} \frac{G M}{R}}\) then the value of \('a'\) is \(....\) [Given: The two planets are fixed in their position]

Two identical symmetric double convex lenses of focal length \(f\) are cut into two equal parts \(L_1, L_2\) by \(A B\) plane and \(L_3, L_4\) by \(X Y\) plane as shown in figure respectively. The ratio of focal lengths of lenses \(L_1\) and \(L_3\) is ________.

An ideal fluid of density \(800 \; kgm ^{-3}\), flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from \(a\) to \(\frac{ a }{2}\). The pressure difference between the wide and narrow sections of pipe is \(4100 \; Pa\). At wider section, the velocity of fluid is \(\frac{\sqrt{x}}{6} \; ms ^{-1}\) for \(x = \dots\) \(\left(\right.\) Given \(g =10 \; m ^{-2}\) )

A prism of angle \(A=1^{\circ}\) has a refractive index \(\mu=1.5 .\) A good estimate for the minimum angle of deviation (in degrees) is close to \(N/10\) Value of \(N\) is......

An infinitely long wire has uniform linear charge density \(\lambda=2 \mathrm{nC} / \mathrm{m}\). The net flux through a Gaussian cube of side length \(\sqrt{3} \mathrm{~cm}\), if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be \(\mathrm{xNm}^2 \mathrm{C}^{-1}\), where x is :
[Neglect any edge effects and use \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\) SI units]

A hydrogen atom makes a transition from \(n = 2\) to  \(n = 1\) and emits a photon. This photon strikes a doubly ionized lithium atom \((z = 3)\)  in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is

An electric dipole of moment \(\overrightarrow{\mathrm{p}}=(-\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \times 10^{-29}\; \mathrm{C} \cdot \mathrm{m}\) is at the origin \((0,0,0) .\) The electric field due to this dipole at \(\overrightarrow{\mathrm{r}}=+\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) (note that \(\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{p}}=0)\) is parallel to

The electric field in an electromagnetic wave is given by \({E}=\left(50\, {NC}^{-1}\right) \sin \omega({t}-{x} / {c})\) The energy contained in a cylinder of volume \({V}\) is \(5.5 \times 10^{-12} \, {J}\). The value of \({V}\) is \(......{cm}^{3}\) \(\left(\right.\) given \(\left.\in_{0}=8.8 \times 10^{-12} \,{C}^{2} {N}^{-1} {m}^{-2}\right)\)

A magnetic dipole in a constant magnetic field has