Physics

On the $x$ -axis and at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by $\frac{Ax}{{\left(x^2+a^2\right)}^{3/2}}$ in the $x$ -direction. The magnitude of gravitational potential on the $x$ -axis at a distance $x$ , taking its value to be zero at infinity is:

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm^-2 . The density of water is 1 gmcm^-3 and water offers negligible drag force on the bubble. The mass of the bubble is: (g=980 cm/s²)

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5
 , while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in $\mathrm{A}\to \mathrm{I}\mathrm{V};\mathrm{}\mathrm{B}\to \mathrm{I}$ ) of the waves are:

Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum:

A small bar magnet placed with its axis at ${30}^{\circ }$ with an external field of $0.06\mathrm{T}$ experiences a torque of $0.018\mathrm{N}\mathrm{m}$ . The minimum work required to rotate it from its stable to unstable equilibrium position is:

A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3{\mathrm{W}\mathrm{m}}^{-2}$ falls normally on a polarizer (cross sectional area $3*{10}^{-4}{\mathrm{m}}^2$ ) which rotates about its axis with an angular speed of $31.4\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}$ . The energy of light passing through the polariser per revolution, is close to:

A telegraph line of length 100km has a capacity of $0.01\mu F/km$  and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that need to be introduced in series is _________mH. (if π = $\sqrt[]{10}$ )

The specific heat of water $=4200\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ and the latent heat of ice $=3.4*{10}^5\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}$ . 100 grams of ice at $0^{\circ }\mathrm{C}$ is placed in $200\mathrm{g}$ of water at ${25}^{\circ }\mathrm{C}$ . The amount of ice that will melt as the temperature of water reaches $0^{\circ }\mathrm{C}$ is close to (in grams):

A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 ke V, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be ________cm.

A wire $A$ , bent in the shape of an arc of a circle, carrying a current of $2\mathrm{A}$ and having radius $2\mathrm{c}\mathrm{m}$ and another wire $B$ , also bent in the shape of arc of a circle, carrying a current of $3\mathrm{A}$ and having radius of $4\mathrm{c}\mathrm{m}$ , are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is: