If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is _________ m.
(Atomic number of gold \(=79\) and \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\)in SI units)

A pulley of radius \(1.5\,m\) is rotated about its axis by a force \(F =\left(12 t -3 t ^{2}\right)\,N\) applied tangentially (while \(t\) is measured in seconds). If moment of inertia of the pulley about its axis of rotation is \(4.5\,kg\,m ^{2}\), the number of rotations made by the pulley before its direction of motion is reversed, will be \(\frac{K}{\pi}\). The value of \(K\) is \(.....\)

The refractive index of the material of a glass prism is \(\sqrt{3}\). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

A ball of mass \(4\, kg\), moving with a velocity of \(10\, ms ^{-1}\), collides with a spring of length \(8\, m\) and force constant \(100\, Nm ^{-1}\). The length of the compressed spring is \(x\, m\). The value of \(x\), to the nearest integer, is ........ .

A transverse wave on a string is described by \(y = 3\sin(36t + 0.018x + \pi/4)\), where \(x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
(\(\pi = 3.14\))

This question has Statement \(-1\) and Statement \(-2.\) Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement \(-1:\) In Young's double slit experiment, the number of fringes observed in the field of view is small With longer wavelength of light and is large with shorter wavelength of light. Statement \(-2:\) In the double slit experiment the fringe width depends directly on the wavelength of light.

The energy \(E\) and momentum \(p\) of a moving body of mass \(m\) are related by some equation. Given that c represents the speed of light, identify the correct equation.

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its \((i)\) second permitted energy level to the first level, and \((ii)\) the highest permitted energy level to the first permitted level.

A light string passing over a smooth light pulley connects two blocks of masses \(m_1\) and \(m_2\) (where \(m_2>m_1\) ). If the acceleration of the system is \(\frac{\mathrm{g}}{\sqrt{2}}\), then the ratio of the masses \(\frac{\mathrm{m}_1}{\mathrm{~m}_2}\) is _______.

An electric dipole of dipole moment \(6 \times 10^{-6} \mathrm{Cm}\) is placed in uniform electric field of magnitude \(10^6 \mathrm{~V} / \mathrm{m}\). Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.