Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance \(2000 \,\Omega\) is used to measure the potential difference across \(500 \,\Omega\) resister, the reading of the voltmeter will be ............... \(V\)

In a double -slit experiment, green light \(\left( {5303\,\mathop A\limits^o } \right)\) falls on a double slit having a separation of \(19.44\,\mu m\) and a width of \(4.05\,\mu m\). The number of bright fringes between the first and the second diffraction minima is

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \(h_{sph}\) and \(h_{cyl}\) on the incline. The radio \(\frac{{{h_{sph}}}}{{{h_{cyl}}}}\) is given by

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 __________.

A particle starts simple harmonic motion from the mean position. Its amplitude is \(a\) and total energy \(E\). At one instant its kinetic energy is \(3E/4.\) Its displacement at that instant is

A \(0.5 \,kg\) block moving at a speed of \(12 \,ms ^{-1}\) compresses a spring through a distance \(30\, cm\) when its speed is halved. The spring constant of the spring will be \(Nm ^{-1}\).

A ball is dropped from the top of a \(100\; m\) high tower on a planet. In the last \(\frac{1}{2}\;s \) before hitting the ground, it covers a distance of \(19\; \mathrm{m}\). Acceleration due to gravity (in \(\mathrm{ms}^{-2}\) ) near the surface on that planet is

Three identical spheres each of mass \(M\) are placed at the corners of a right angled triangle with mutually perpendicular sides equal to \(3\,m\) each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be \(\sqrt{x} m\). The value of \(x\) is

The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then

Two electric dipoles \(A, B\) with respective dipole moments \(\overrightarrow {{d_A}}  =  - 4\,qa\,\hat i\) and \(\overrightarrow {{d_B}}  =  2\,qa\,\hat i\) are placed on the \(x-\) axis with a separation \(R\), as shown in the figure. The distance from \(A\) at which both of them produce the same potential is

Activities of three radioactive substances \(A , B\) and \(C\) are represented by the curves \(A, B\) and \(C,\) in the figure. Then their half-lives \(T _{\frac{1}{2}}( A ): T _{\frac{1}{2}}( B ): T _{\frac{1}{2}}( C )\) are in the ratio

In the given circuit, the breakdown voltage of the Zener diode is \(3.0 \mathrm{~V}\). What is the value of \(\mathrm{I}_z\) ?