Physics

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):

A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of 10² As⁻¹. The value of the potential difference Vₚ - Vq, (in volts) at that instant, is

Initially a gas of diatomic molecules is contained in a cylinder of volume V₁ at a pressure P₁ and temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a volume 2V₁, is given by P₂. The ratio P₂/P₁ is

Suppose that intensity of a laser is (315/π) W/m². The rms electric field, in units of V/m associated with this source is close to the nearest integer is (ε₀ = 8.86 * 10⁻¹² C²N⁻¹m⁻²; c = 3 * 10⁸ ms⁻¹)

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is