A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is on

A potential divider circuit is shown in figure. The output voltage \(V_0\) is _______.

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is _______.

If momentum \([ P ]\), area \([ A ]\) and time \([ T ]\) are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

The magnetic intensity at the centre of a long current carrying solenoid is found to be \(1.6 \times 10^3 Am ^{-1}\). If the number of turns is 8 per cm, then the current flowing through the solenoid is \(................\,A\)

Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) is

In the network shown below, the charge accumulated in the capacitor in steady state will be ........... \(\mu C\)

A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be

A solenoid of \(1000\) turns per metre has a core with relative permeability \(500\). Insulated windings of the solenoid carry an electric current of \(5\, A\). The magnetic flux density produced by the solenoid is (permeability of free space \(\left.=4 \pi \times 10^{-7} H / m \right)\)

A bob of mass \(m\) attached to an inextensible string of length \(l\) is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed \(\omega\ rad/s\) about the vertical. About the point of suspension:

The displacement and the increase in the velocity of a moving particle in the time interval of \(t\) to \((t+1) \mathrm{s}\) are \(125 \mathrm{~m}\) and \(50 \mathrm{~m} / \mathrm{s}\), respectively. The distance travelled by the particle in \((\mathrm{t}+2)^{\mathrm{th}} \mathrm{s}\) is __________ \(\mathrm{m}\).