The volume of an ideal gas \((\gamma=1.5)\) is changed adiabatically from \(5\) litres to \(4\) litres. The ratio of initial pressure to final pressure is _______.

A wire of length \(L\) and mass per unit length \(6.0\times 10^{-3}\; \mathrm{kgm}^{-1}\) is put under tension of \(540\; \mathrm{N}\). Two consecutive frequencies that it resonates at are : \(420\; \mathrm{Hz}\) and \(490 \;\mathrm{Hz}\). Then \(\mathrm{L}\) in meters is

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed: \(A.\) By changing the magnitude of the magnetic field within the coil. \(B.\) By changing the area of coil within the magnetic field. \(C.\) By changing the angle between the direction of magnetic field and the plane of the coil. \(D.\) By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below

A solid cylinder and a solid sphere, having same mass \(M\) and radius \(R\), roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be.

A gas molecule of mass \(M\) at the surface of the Earth has kinetic energy equivalent to \(0\,^oC\). If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (\(k_B\) is Boltzmann constant)

The angular frequency of alternating current in a \(L-C-R\) circuit is \(100\, rad / s\). The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current \(I=10 \sin (\omega t ) A\), where \(\omega=1000 rad . / s\). A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed \(v =1 cm / s\). The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is \(\alpha / \sqrt{2} \quad \mu A\). The value of \(\alpha\) is ___________.
[Resistance of the loop \(=10 \Omega\) ]

A galvanometer having a coil resistance \(100 \;\Omega\) gives a full scale deflection when a current of \(1 \;\mathrm{mA}\) is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of \(10\; \mathrm{V} ?\)......\(k\Omega\)

The electric field in a region of space is given by, \(\overrightarrow E  = {E_0}\hat i + 2{E_0}\hat j\) where \(E_0\, = 100\, N/C\). The flux of the field through a circular surface of radius \(0.02\, m\) parallel to the \(Y-Z\) plane is nearly

For three low density gases \(A, B, C\) pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure. The temperature corresponding to the point ' \(K\) ' is \(...........\,{}^{\circ}\,C\)

Charge is distributed within a sphere of radius \(R\) with a volume charge density \(\rho (r) = \frac{A}{{{r^2}}}{e^{ - 2r/a}}\) where \(A\) and \(a\) are constants. If \(Q\) is the total charge of this charge distribution, the radius \(R\) is.