A particle of mass \(20\,g\) is released with an initial velocity \(5\,m/s\) along the curve from the point \(A,\) as shown in the figure. The point \(A\) is at height \(h\) from point \(B.\) The particle slides along the frictionless surface. When the particle reaches point \(B,\) its angular momentum about \(O\) will be ......... \(kg - m^2/s\). [Take \(g = 10\,m/s^2\) ]

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is \(1\,kg\), the angular frequency is \(\omega_1\). When the mass block is \(2\,kg\) the angular frequency is \(\omega_2\). The ratio \(\omega_2 / \omega_1\) is

A particle having charge \(10^{-9}\) C moving in \(x\)-\(y\) plane in fields of \(0.4\hat{j}\) N/C and \(4 \times 10^{-3} \hat{k}\) T experiences a force of \((4\hat{i} + 2\hat{j}) \times 10^{-10}\) N. The velocity of the particle at that instant is _______ m/s.

Consider the efficiency of Carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.

A diatomic gas \((\gamma=1.4)\) does \(200 \mathrm{~J}\) of work when it is expanded isobarically. The heat given to the gas in the process is _______.

A monochromatic neon lamp with wavelength of \(670.5\, {nm}\) illuminates a photo-sensitive material which has a stopping voltage of \(0.48\, {V}\). What will be the stopping voltage if the source light is changed with another source of wavelength of \(474.6 \,{nm} ?\) (In \({V}\))

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ___________ cm.

Three equal masses \(m\) are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At \(t=0\), they are given an initial velocity \(\vec{V}_A=V_0 \overrightarrow{A C}, \vec{V}_B=V_0 \overrightarrow{B A}\) and \(\vec{V}_C=V_0 \overrightarrow{C B}\). Here, \(\overrightarrow{A C}, \overrightarrow{C B}\) and \(\overrightarrow{B A}\) are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

If a body of mass \(1\) kg falls on the earth from infinity, it attains velocity \((v)\) and kinetic energy \((k)\) on reaching the surface of earth. The values of \(v\) and \(k\) respectively are _______. (Take radius of earth to be \(6400\) km and \(g = 9.8\) m/s\(^2\))

A magnet hung at \(45^{\circ}\) with magnetic meridian makes an angle of \(60^{\circ}\) with the horizontal. The actual value of the angle of dip is.

A planet revolving in elliptical orbit has \((A)\) a constant velocity of revolution. \((B)\) has the least velocity when it is nearest to the sun. \((C)\) its areal velocity is directly proportional to its velocity. \((D)\) areal velocity is inversely proportional to its velocity. \((E)\) to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below