The acceleration due to gravity on the surface of earth is \(g\). If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

A block of mass \(2\,kg\) is attached with two identical springs of spring constant \(20\,N / m\) each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is \(\frac{\pi}{\sqrt{x}}\) in SI unit. The value of \(x\) is \(..........\)

Four identical particles of mass \(M\) are located at the corners of a square of side \(‘a’\). What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the square?

Every planet revolves around the sun in an elliptical orbit : \(A.\) The force acting on a planet is inversely proportional to square of distance from sun. \(B.\) Force acting on planet is inversely proportional to product of the masses of the planet and the sun \(C.\) The centripetal force acting on the planet is directed away from the sun. \(D.\) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below :

A hydrogen atom in its ground state absorbs \(10.2\ eV\) of energy. The orbital angular momentum is increased by (Given Planck constant \(h = 6.6 \times {10^{ - 34}}J -  sec\))

A common emitter amplifier circuit, built using an \(npn\) transistor, is shown in the figure. Its \(dc\) current gain is \(250\), \(R_C = 1\,k\, \Omega \) and \(V_{CC} = 10\,V\). What is the minimum base current for \(V_{CE}\) to reach saturation?.........\(\mu A\)

A block of ice of mass \(120\,g\) at temperature \(0^{\circ} C\) is put in \(300\,gm\) of water at \(25^{\circ} C\). The \(xg\) of ice melts as the temperature of the water reaches \(0^{\circ} C\). The value of \(x\) is [Use: Specific heat capacity of water \(=4200\) \(J\,kg ^{-1} K ^{-1}\), Latent heat of ice \(\left.=3.5 \times 10^{5} J\,kg ^{-1}\right]\)

When the wavelength of radiation falling on a metal is changed from \(500 \,nm\) to \(200\, nm ,\) the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to\(.....eV\)

A long solenoid of radius \(\mathrm{R}\) carries a time \((t)-\)dependent current \(\mathrm{I}(\mathrm{t})=\mathrm{I}_{0} \mathrm{t}(1-\mathrm{t})\). A ring of radius \(2 \mathrm{R}\) is placed coaxially near its middle. During the time interval \(0 \leq t \leq 1\), the induced current \(\left(\mathrm{I}_{\mathrm{R}}\right)\) and the induced \(\mathrm{EMF}\left(\mathrm{V}_{\mathrm{R}}\right)\) in the ring change as

A body of mass \(2\) kg begins to move under the influence of time dependent force \(\vec{F} = (2t\hat{i} + 6t^2\hat{j})\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\)-axis respectively. The power produced by the force at \(t = 2\) s is _____ W.

The charge flowing in a conductor changes with time as \(Q ( t )=\alpha t -\beta t ^2+\gamma t ^3\). Where \(\alpha, \beta\) and \(\gamma\) are constants. Minimum value of current is :

A particle of mass \(\mathrm{m}\) is projected with a speed \(u\) from the ground at an angle \(\theta=\frac{\pi}{3}\) w.r.t. horizontal (\(x-\)axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity \(u \hat i\). The horizontal distance covered by the combined mass before reaching the ground is

In the given figure, the \(emf\) of the cell is \(2.2\, {V}\) and if internal resistance is \(0.6\, \Omega\). Calculate the power dissipated in the whole circuit: (in \(W\))