In the equation \(\left[X+\frac{a}{Y^2}\right][Y-b]= R T, X\) is pressure, \(Y\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The physical quantity equivalent to the ratio \(\frac{a}{b}\) is

The plot given below is of the average power delivered to an \(LRC\) circuit versus frequency. The quality factor of the circuit is

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its werght on the surface of earth is \(200\,N\), will be \(...........\,N\) ( \(Given R =\) Radrus of earth)

A transmitting station releases waves of wavelength \(960\, m\). A capacitor of \(2.56\, \mu F\) is used in the resonant circuit. The self inductance of coil necessary for resonance is ............. \(-\times 10^{-8} H\)

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass \(=500\, g\), Decay constant \(=20 \,g / s\) then ...... \(s\) time is required for the amplitude of the system to drop to half of its initial value ? \((\ln 2=0.693)\)

As shown in the figure, a point charge \(Q\) is placed at the centre of conducting spherical shell of inner radius a and outer radius \(b\). The electric field due to charge \(Q\) in three different regions I, II and III is given by: \(( I : r < a , II : a < r < b , III : r > b )\)

A current of \(2\, mA\) was passed through an unknown resistor which dissipated a power of \(4.4\, W\). Dissipated power when an ideal power supply of \(11\, V\) is connected across it is

Consider the following logic circuit.

The output is \(\mathrm{Y}=0\) when :

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

In the given figure, the block of mass \(m\) is dropped from the point ' \(A\) '. The expression for kinetic energy of block when it reaches point ' \(B\) ' is ................

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity \(\omega\). A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If \(E\) be the initial Kinetic energy of the system, then final Kinetic energy will be \(\frac{E}{x}\).The value of \(x\) is \(....\)

A wire carrying current \(I\) is tied between points \(P\) and \(Q\) and is in the shape of a circular arc of radius \(R\) due to a uniform magnetic field \(B\) (perpendicular to the plane of the paper, shown by \(\times \times \times \)) in the vicinity of the wire. If the wire subtends an angle \(2\theta_0\) at the centre of the circle (of which it forms an arc) then the tension in the wire is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Knowing initial position \(x_0\) and initial momentum \(p_0\) is enough to determine the position and momentum at any time \(t\) for a simple harmonic motion with a given angular frequency \(\omega\).
Reason (R): The amplitude and phase can be expressed in terms of \(x_0\) and \(\mathrm{p}_0\).
In the light of the above statements, choose the correct answer from the options given below :