A metre scale is balanced on a knife edge at its centre. When two coins, each of mass \(10\, g\) are put one on the top of the other at the \(10.0\, cm\) mark the scale is found to be balanced at \(40.0\, cm\) mark. The mass of the metre scale is found to be \(x \times 10^{-2}\) \(kg\). The value of \(x\) is

An electric bulb of \(500 \,watt\) at \(100\, volt\) is used in a circuit having a \(200\, {V}\) supply. Calculate the resistance \({R}\) to be connected in series with the bulb so that the power delivered by the bulb is \(500\, {W}\). (in \(\Omega\))

Which one of the following is not a measurable quantity ?

A \(70\, kg\) man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force \(F\) to raise himself The center of gravity rises by \(0.5\, m\) before he leaps. After the leap the \(c.g.\) rises by another \(1\, m\). The maximum power delivered by the muscles is : (Take \(g\, = 10\, ms^{-2}\))

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

A particle is executing Simple Harmonic Motion \((SHM)\). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

A parallel plate capacitor is of area \(6\, cm^2\) and a separation \(3\, mm\). The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants \(K_1 = 10, K_2 = 12\) and \(K_3 = 14\). The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be

When a coil is placed in a time dependent magnetic field the power dissipated in it is \(P\). The number of turns, area of the coil and radius of the coil wire are \(N\), \(A\) and \(r\) respectively. For a second coils number of turns, area of the coil and radius of the coil wire are \(2N\), \(2A\) and \(3r\) respectively. When the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2}\,\alpha P\). The value of \(\alpha\) is _______.

The susceptibility of a paramagnetic material is \(99\) . The permeability of the material in \(Wb / A - m\) is : [Permeability of free space \(\left.\mu_{0}=4 \pi \times 10^{-7} Wb / A -m\right]\)