The actual value of resistance \(R\), shown in the figure is \(30\,\Omega \). This is measured in an experiment as shown using the standard formula \(R = \frac{V}{I}\) where \(V\) and \(I\) are the readings of the voltmeter and ammeter, respectively. If the measured value of \(R\) is \(5\%\) less, then the internal resistance of the voltmeter is ................. \(\Omega\)

In an alpha particle scattering experiment distance of closest approach for the \(\alpha\) particle is \(4.5 \times 10^{-14} \mathrm{~m}\). If target nucleus has atomic number \(80\) , then maximum velocity of \(\alpha\)-particle is _______ \(\times 10^5\) \(\mathrm{m} / \mathrm{s}\) approximately. \(\left(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}\right.\) unit, mass of \(\alpha\) particle \(=\) \(\left.6.72 \times 10^{-27} \mathrm{~kg}\right)\)

The distance of the Sun from earth is \(1.5 \times 10^{11} \,m\) and its angular diameter is \((2000) \,s\) when observed from the earth. The diameter of the Sun will be ...........

Two cells of emfs \(1\) V and \(2\) V and internal resistance \(2\,\Omega\) and \(1\,\Omega\), respectively connected in parallel, gave a current of \(1\) A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be \(\dfrac{\alpha}{5}\) A. The value of \(\alpha\) is __________.

Magnetic fields at two points on the axis of a circular coil at a distance of \(0.05\, m\) and \(0.2\, m\) from the centre are in the ratio \(8: 1.\) The radius of coil is .......... \(m\)

A cylinder is rolling down on an inclined plane of inclination \(60^{\circ}\). It's acceleration during rolling down will be \(\frac{\mathrm{x}}{\sqrt{3}} \mathrm{~m} / \mathrm{s}^2\), where \(\mathrm{x}=\)___________. (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ).

Two cars are travelling towards each other at speed of \(20 \mathrm{~m} \mathrm{~s}^{-1}\) each. When the cars are \(300 \mathrm{~m}\) apart, both the drivers apply brakes and the cars retard at the rate of \(2 \mathrm{~m} \mathrm{~s}^{-2}\). The distance between them when they come to rest is _______.

The equation of current in a purely inductive circuit is \(5 \sin \left(49 \pi t-30^{\circ}\right)\). If the inductance is \(30\,mH\) then the equation for the voltage across the inductor, will be.\(\left\{\right.\) Let \(\left.\pi=\frac{22}{7}\right\}\)

Two conducting circular loops \(A \) and \(B\) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is _______.

A steel rail of length \(5\,m\) and area of cross-section \(40\,cm^2\) is prevented from expanding along its length while the temperature rises by \(10\,^oC\). If coefficient of linear expansion and Young's modulus of steel are \(1.2\times10^{-5}\, K^{-1}\) and \(2\times10^{11}\, Nm^{-2}\) respectively, the force developed in the rail is approximately

A closed organ pipe has a fundamental frequency of \(1.5\, kHz\). The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is \(20,000\, Hz\))

An engine is attached to a wagon through a shock absorber of length \(1.5\, {m}\). The system with a total mass of \(40,000\, {kg}\) is moving with a speed of \(72\, {kmh}^{-1}\) when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by \(1.0\, {m}\). If \(90\, \%\) of energy of the wagon is lost due to friction, the spring constant is \(....\, \times 10^{5}\, {N} / {m}\)