Physics Test 29...

A train of weight 10⁷ N is running on a level track with a uniform speed of 36 km h⁻¹. The frictional force is 0.5 kg f per quintal.

Taking g = 10 ms⁻², the power of the engine is:

The electric potential at a point (x,y) in the x-y plane is given by V = −Kxy

The electric field intensity at a distance r from the origin varies as

A dipole of electric dipole moment p is placed in a uniform electric field of strength E.

If θ is the angle between positive directions of p and E, then the potential energy of the electric dipole is largest when θ is:

Two slits are separated by a distance of 0.5mm and illuminated with light of wavelength  . If the screen is placed at 2.5m from the slits.

The distance of the third bright fringe from the centre will be

22g of carbon dioxide at 27^∘C is mixed in a closed container with 16g of oxygen at 37^∘C.

The temperature of the mixture (neglect vibrational degree of freedom)

2L of water in a container is heated with a coil of 1kW at 27^∘C . The lid of the container is open and energy dissipates at rate of 160Js⁻¹. Find the time after which temperature will rise from 27^∘C to 77^∘C?

[Given specific heat of water is 4.2kJ/kg]

A solid, uniform cube of side a and mass M is placed on a fixed, horizontal, perfectly rough surface. A small, point–mass m is fixed to the midpoint of one upper edge of the cube. The cube is now given an infinitesimal push so that it begins to topple about the edge in contact with the ground. Find the minimum coefficient of friction μ_min that will permit the cube to topple completely (i.e. until the adjacent edge touches the ground) without ever slipping on the surface. Assume gravitational acceleration g and ignore air drag. (Take m ≪ M, so the cube’s centre-of-mass remains at its geometric centre.)

Spacing between the two slits,  d  = 0.1 mm

Distance of screen from the slits,  D  = 1.0 m

Wavelength of light,  λ  = 5000 Å

Fringe width,  β

The power used is :-

The time period of oscillation of a simple pendulum of length l is T₁ and the time period of oscillation of a uniform rod of the same length l pivoted at one end and oscillating in a vertical plane is T₂. Amplitude of oscillations in both the cases is small.