The current \(I\) flowing through the given circuit will be \(.....A\).

A particle of mass \(1\, {kg}\) is hanging from a spring of force constant \(100\, {Nm}^{-1 .}\) The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period \({T}\). The time when the kinetic energy and potential energy of the system will become equal, is \(\frac{{T}}{{x}}\). The value of \({x}\) is ..... .

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is \(\mathrm{P} \times 10^{11} \mathrm{Nm}^{-2}\), where the value of P is: (Take \(\left.\mathrm{g}=3 \pi \mathrm{~m} / \mathrm{s}^2\right)\)

There is a small source of light at some depth below the surface of water (refractive index \(=\frac{4}{3}\) ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly)...........\(\%\) [Use the fact that surface area of a spherical cap of height \(\mathrm{h}\) and radius of curvature \(\mathrm{r} \text { is } 2 \pi \mathrm{rh}]\)

Two iron solid discs of negligible thickness have radius \(R_1\) and \(R_2\) and moment of intertia \(I_1\) and \(I_2\), respectively. For \(R_2=2 R_1\), the ratio of \(I_1\) and \(I_2\) would be \(1 / x\), where \(\mathrm{x}=\) ________ -

The acceleration due to gravity on the surface of earth is \(g\). If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

The average kinetic energy of a molecule of the gas is

A ball of mass \(200\,g\) rests on a vertical post of height \(20\,m\). A bullet of mass \(10\,g\), travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance \(30\,m\) and the bullet at a distance of \(120\,m\) from the foot of the post. The value of initial velocity of the bullet will be \(............m/s\) (if \(\left.g =10 m / s ^2\right)\)

A single slit of width \(b\) is illuminated by a coherent monochromatic light of wavelength \(\lambda \). If the second and fourth minima in the diffraction pattern at a distance \(1\,m\) from the slit are at \(3\, cm\) and \(6\, cm\) respectively from the central maximum, what is the width of the central maximum ?......\(cm\) (i.e. distance between first minimum on either side of the central maximum)

Sixty four conducting drops each of radius \(0.02 m\) and each carrying a charge of \(5 \,\mu C\) are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be ............

The \(SI\) unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be ..............