Two particles carrying equal charges move parallel to each other with the speed \(150 \mathrm{~km} / \mathrm{s}\). If \(\mathbf{F}_1\) and \(\mathbf{F}_2\) are magnetic and electric forces between two charged particles then, \(\frac{\left|\mathbf{F}_1\right|}{\left|\mathbf{F}_2\right|}\) is \(\left(\right.\) Let \(\left.\mu_0 \varepsilon_0=\frac{1}{9 \times 10^{16}} \mathrm{~s}^2 / \mathrm{m}^2\right)\)

The horizontal and vertical displacements of a projectile at time \(t\) are \(x=36 t\) and \(y=48 t-4.9 t^2\), respectively. Initial velocity of the projectile in \(\mathrm{m} / \mathrm{s}\) is

A circuit is shown in the following figure for which $C_1=(3\pm 0.011)\mu \mathrm{F},C_2=(5\pm 0.01)\mu \mathrm{F}$ and $C_3=(1\pm 0.01)\mu \mathrm{F}.$If $C$ is the equivalent capacitance across $AB,$then $C$ is given by

Water is pumped steadily out of a flooded basement, at the speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ through a hose (tube) of radius, $1 \mathrm{cm},$ passing through a window, $3 \mathrm{m}$ above the water level. The power of the pump is (Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, density of water $=1000 \mathrm{kg} {\mathrm{m}}^{-3}$)

A thin wire of length \(l\) having density \(\rho\) is bent into a circular loop with \(C\) as its centre, as shown in figure. The moment of inertia of the loop about the line \(A B\) is

In a transistor circuit, when the base current is increased by 50 micro-amperes keeping the collector voltage fixed at 2 volts, the collector current increases by \(1 \mathrm{~mA}\). The current gain of the transistor is

The magnetic field at a point P on the axis of a short bar magnet of magnetic moment M is B. If another short bar magnet of magnetic moment 2 M is placed on the first magnet such that their axes are perpendicular and their centres coincide. The resultant magnetic field at the point P due to both the magnets is

How much thermal energy is required to change a \(40 \mathrm{~g}\) ice cube from solid at \(-10^{\circ} \mathrm{C}\) to steam at \(110^{\circ} \mathrm{C}\) ? [Assume, latent heat of fusion for water \(=80 \mathrm{kcal} / \mathrm{kg}\), specific heat of water \(=1 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}\), specific heat of ice \(=0.5 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}\), specific heat of steam \(=0.48 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}\), latent heat of vaporisation of water \(\left.=540 \mathrm{kcal} / \mathrm{kg}^{\circ} \mathrm{C}\right]\)

A metal cube absorbs $2100.0 \mathrm{J}$ of heat when its temperature is raised by $2 °\mathrm{C}$. If the specific heat of the metal is $900 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$, then the mass of the cube is

A particle leaves the origin with initial velocity $\overrightarrow{v}=\left(3\hat{\mathrm{i}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ and a constant acceleration $\overrightarrow{a}=\left(-1\hat{\mathrm{i}}-0.5\hat{\mathrm{j}}\right)\mathrm{m} {\mathrm{s}}^{-2}$. The position vector of particle, when it reaches its maximum $x$-coordinate, is

Radiations of wavelength \(400 \mathrm{~nm}\) incidents on a photo sensitive material of work function \(2.2 \mathrm{eV}\). The stopping potential is nearly

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

There are two holes one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is \(0.01 \mathrm{~m}^2\) and the vertical distance between the holes is one metre. The tank is filled with water.The net force on the tank in newton when the water flows out of the holes is (Density of water \(=1000 \mathrm{~kg} / \mathrm{m}^3\) )