\(0.056 \,kg\) of Nitrogen is enclosed in a vessel at a temperature of \(127\,^{\circ} C\). The amount of heat required to double the speed of its molecules is k cal. (Take \(R =2\) \(cal \,mole\) \(^{-1} K ^{-1}\) )

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility \(\left.\chi_{\mathrm{mg}}=1.2 \times 10^{-5}\right)\) is :

Two solids \(A\) and \(B\) of mass \(1\, kg\) and \(2\, kg\) respectively are moving with equal linear momentum. The ratio of their kinetic energies \((K.E.)_{ A }:( K.E. )_{ B }\) will be \(\frac{ A }{1},\) so the value of \(A\) will be ..... .

This questions has Statement \(I\) and Statement \(II\) Of the four choices given after the Statements, choose the one that best describes into two Statements.
Statement\(-I\) : Higher the range, greater is the resistance of ameter.
Statement\(-II\) : To increase the range of ammeter, additional shunt needs to be used across it.

The relation between time \(t\) and distance \(x\) for a moving body is given as \(t=m x^{2}+n x\), where \({m}\) and \({n}\) are constants. The retardation of the motion is - (Where \(v\) stands for velocity)

Three point particles of masses \(1.0\; \mathrm{kg} .1 .5 \;\mathrm{kg}\) and \(2.5\; kg\) are placed at three comers of a right angle triangle of sides \(4.0\; \mathrm{cm}, 3.0 \;\mathrm{cm}\) and \(5.0\; \mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point

The radius of fifth orbit of the \(L ^{++}\)is \(.........\times 10^{-12}\,m\). Take : radius of hydrogen atom \(=0.51 \mathring A\)

A LCR series circuit driven with \(E_{rms} = 90\) V at frequency \(f_d = 30\) Hz has resistance \(R = 80\,\Omega\), an inductance with inductive reactance \(X_L = 20.0\,\Omega\) and capacitance with capacitive reactance \(X_C = 80.0\,\Omega\). The power factor of the circuit is _______.

Two bodies of masses \(m_{1}=5\,kg\) and \(m _{2}=3\,kg\) are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass \(m _{1}\) will be\(....N\) [Take \(g=10\,ms ^{-2}\) ]

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

A rod of mass \(‘M’\) and length \(‘2L’\) is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of \(‘m’\) are attached at distance \(‘L/2’\) from its centre on both sides, it reduces the oscillation frequency by \(20\%\). The value of ratio \(m/M\) is close to