Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is \(\frac{\sqrt{x}}{2}\). Then, the value of \(x\) is .... .

Bob of a simple pendulum of length \(l\) is made of iron . The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is \(T\) then

Ratio of thermal energy released in two resistor \(R\) and \(3 R\) connected in parallel in an electric circuit is :

The distance between charges \(+\mathrm{q}\) and \(-\mathrm{q}\) is \(2 l\) and between \(+2 \mathrm{q}\) and \(-2 \mathrm{q}\) is \(4 l\). The electrostatic potential at point \(P\) at a distance \(r\) from centre \(O\) is \(-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}\), where the value of \(\alpha\) is _______. (Use \(\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)\)

The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\)

The \(K_{\alpha}\; X-\)ray of molybdenum has wavelength \(0.071\, {nm}\). If the energy of a molybdenum atoms with a \(K\) electron knocked out is \(27.5\, {keV}\), the energy of this atom when an \(L\) electron is knocked out will be \(....\,keV.\) (Round off to the nearest integer) \(\left[{h}=4.14 \times 10^{-15} \,{eVs}, {c}=3 \times 10^{8}\, {ms}^{-1}\right.]\)

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is \(25 \%\) of the velocity of light, then the ratio of \(K.E.\) of electron and \(K.E.\) of photon will be:

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at \(27^{\circ}\,C\) is \(............^{\circ}\,C\)

Dimensions of universal gravitational constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are _______.

For the circuit shown below, calculate the value of \({I}_{{z}}\) : (In \({mA}\))

A block takes \(t\) time to slide down a plane inclined at \(45°\) to the horizontal. If the surface is made smooth (frictionless), the block takes time \(\dfrac{t}{2}\) to slide down the plane. The coefficient of friction between the block and the inclined plane is \(\left(\dfrac{\alpha}{100}\right)\). The value of \(\alpha\) is __________.

The velocity of the bullet becomes one third after it penetrates \(4\,cm\) in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at \((4+x)\,cm\) inside the block. The value of \(x\) is\(.....\)