A \(110 \; V , 50 \; Hz , AC\) source is connected in the circuit (as shown in figure). The current through the resistance \(55 \; \Omega\), at resonance in the circuit, will be \(\dots \; A\).

A satellite is moving with a constant speed \(v\) in circular orbit around the earth. An object of mass \(‘m’\) is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

Arrange the following in the ascending order of wavelength : \((A)\) Gamma rays \(\left(\lambda_1\right)\) \((B)\) x-ray \(\left(\lambda_2\right)\) \((C)\) Infrared waves \(\left(\lambda_3\right)\) \((D)\) Microwaves \(\left(\lambda_4\right)\) Choose the most appropriate answer from the options given below :

An \(AC\) source is connected to an inductance of \(100\,mH\) a capacitance of \(100\,\mu F\) and a resistance of \(120\,\Omega\) as shown in figure. The time in which the resistance having a thermal capacity \(2\,J^{\circ } C\) will get heated by \(16^{\circ} C\) is ..........\(S\)

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio \(2:2:3\). The two pieces of equal masses fly off perpendicular to each other with a speed of \(18~m/s\) each. The velocity of the heavier fragment is ___________ \(m/s\).

For the given circuit, comment on the type of transformer used:

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )

A copper block of mass \(5.0\, kg\) is heated to a temperature of \(500^{\circ} C\) and is placed on a large ice block. What is the maximum amount of ice (ઇન \(kg\)) that can melt? [Specific heat of copper: \(0.39\, Jg ^{-1 \circ} C ^{-1}\) and latent heat of fusion of water : \(335 \,J g ^{-1}\) ]

A \(10\,m\) long horizontal wire extends from North East to South West. It is falling with a speed of \(5.0\,ms^{-1},\) at right angles to the horizontal component of the earth’s magnetic field, of \(0.3\times 10^{-4}\,Wb/m^2\). The value of the induced \(emf\) in wire is 

An open glass tube is immersed in mercury in such a way that a length of \(8\ cm\) extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional \(46\ cm\). What will be length of the air column above mercury in the tube now ....... \(cm\) ? ( Atmospheric pressure = \(76\ cm\) of \(Hg\))

The magnetic field of an electromagnetic wave is given by \(\vec B = 1.6 \times {10^{ - 6}}\,\cos \,\left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\hat i + \hat j} \right)\frac{{Wb}}{{{m^2}}}\) The associated electric field will be