The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of \(176 rad / s\). The frequency of this simple harmonic oscillator is _________ Hz. \(\left[\right.\) take \(\left.\pi=\frac{22}{7}\right]\)

Given below are two statements; one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) Electromagnets are made of soft iron. Reason \(R:\) Soft iron has high permeability and low retentivity. In the light of above, statements, choose the most appropriate answer from the options given below.

The magnetic field at the centre of a circular coil of radius \(I\), due to current I flowing through it, is \(B\). The magnetic field at a point along the axis at a distance \(\frac{r}{2}\) from the centre is

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea \((7.8\, mm)\). This surface separates two media of refractive indices \(1\) and \(1.34\). Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.......\(cm\)

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)
(\(\pi = 3.14\))

A wire having a linear mass density \(9.0 \times 10^{-4} \;{kg} / {m}\) is stretched between two rigid supports with a tension of \(900\; {N}\). The wire resonates at a frequency of \(500\;{Hz}\). The next higher frequency at which the same wire resonates is \(550\; {Hz}\). The length of the wire is \(...... {m}\)

Each side of a box made of metal sheet in cubic shape is \('a'\) at room temperature \('T'\), the coefficient of linear expansion of the metal sheet is \(^{\prime} \alpha^{\prime}\). The metal sheet is heated uniformly, by a small temperature \(\Delta T\), so that its new temperature is \(T +\Delta T\). Calculate the increase in the volume of the metal box.

In an ideal gas at temperature \(T,\)  the average force that a molecule applies on the walls of a closed container depends on \(T\) as \(T^q\) . A good estimate for \(q\) is

A uniform cylinder of mass \(M\) and radius \(R\) is to be pulled over a step of height \(a (a < R\)) by applying a force \(F\) at its centre \('O'\) perpendicular to the plane through the axes of the cylinder on the edge of the step ( see figure). The minimum value of \(F\) required is 

A monochromatic light wave with wavelength \(\lambda_1\) and frequency \(v_1\) in air enters another medium. If the angle of incidence and angle of refraction at the interface are \(45^{\circ}\) and \(30^{\circ}\) respectively, then the wavelength \(\lambda_2\) and frequency \(v_2\) of the refracted wave are :

\(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is

A bullet of mass \(20\,g\) has an initial speed of \(1\,ms^{-1}\) just before it starts penetrating a mud wall of thickness \(20\,cm.\) If the wall offers a mean resistances of \(2.5 \times 10^{-2}\,N,\) the speed of the bullet after emerging from the other side of the wall is close to .............. \(\mathrm{ms}^{-1}\)

A compressive force, \(F\) is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by \(\Delta T\). The net change in its length is zero. Let \(l\) be the length of the rod, \(A\) its area of cross- section, \(Y\) its Young's modulus, and \(\alpha \) its coefficient of linear expansion. Then, \(F\) is equal to