A solid sphere of mass \(500\,g\) and radius \(5\,cm\) is rotated about one of its diameter with angular speed of \(10\,rad \, s ^{-1}\). If the moment of inertia of the sphere about its tangent is \(x \times 10^{-2}\) times its angular momentum about the diameter. Then the value of \(x\) will be ..............

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius \(0.5 \times 10^{-10}\,m\). If the speed of electron is \(2.2 \times 10^{6} \;{m} / {s}\), then the current associated with the electron will be \(....\,\times 10^{-2} \;{mA}\). [Take \(\pi\) as \(\left.\frac{22}{7}\right]\)

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity \(\rho_{ C }, \rho_{ T }, \rho_{ M }\) and \(\rho_{ A }\) espectively Then:

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is :

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is \(30 \;\mathrm{cm}\) and the refractive index of the lens material is \(1.5 .\) then the focal length of the lens (in \(\mathrm{cm}\) ) is

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have _________.

If the time period \(t\) of the oscillation of a drop of liquid of density \(d\), radius \(r\), vibrating under surface tension \(s\) is given by the formula \(t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} \) . It is observed that the time period is directly proportional to \(\sqrt {\frac{d}{s}} \) . The value of \(b\) should therefore be

When kinetic energy of a body becomes \(36\) times of its original value, the percentage increase in the momentum of the body will be _______.

An object is at a distance of \(20\,m\) from a convex lens of focal length \(0.3\,m.\) The lens forms an image of the object. If the object moves away from the lens at a speed of \(5\,m/s,\) the speed and direction of the image will be

The figure shows two solid discs with radius \({R}\) and \({r}\) respectively. If mass per unit area is same for both, what is the ratio of \({MI}\) of bigger disc around axis \({AB}\) (Which is \(\perp\) to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given \('M'\) is the mass of the larger disc. (\(MI\) stands for moment of inertia)

In the reported figure, heat energy absorbed by a system in going through a cyclic process is \(......\,\pi J\)

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \(7^{\text{th}}\) Vernier division coincides with a main scale reading. If the value of \(1\) main scale division is \(1\) mm and there are \(10\) Vernier scale divisions, then the Vernier caliper has