Physics

A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y = Cx² and rotating with angular speed ω (see figure). The value of ω is (neglect friction)

Consider four conducting materials copper, tungsten, mercury and aluminum with resistivity ρc, ρt, ρm and ρa respectively. Then

Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source (λ = 632.8 nm). The distance between the screen and the slits is 100 cm. If a bright fringe is observed on a screen at distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close to:

The mass density of a spherical galaxy varies as K/r over a large distance 'r' from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre 'O' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:

The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of cylinder the zero of the vernier scale is between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)

A charged particle (mass m and charge q) moves along x axis with velocity V₀. When it passes through the origin it enters a region having uniform electric field E = -Ej which extends upto x = d. Equation of path of electron in the region x > d is:

Two identical strings X and Z made of same material have tension Tₓ and T₂ in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio Tₓ/Tz is:

Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

A plane electromagnetic wave, has frequency of 2.0 * 10¹⁰ Hz and its energy density is 1.02 * 10⁻⁸ J/m³ in vacuum. The amplitude of the magnetic field of the wave is close to (1/(4πε₀) = 9 * 10⁹ Nm²/C² and speed of light = 3 * 10⁸ ms⁻¹):