Physics

Two balls of same mass and carrying equal charge are hung by threads of length $l$ from a fixed support. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$  between the balls is proportional to:

Initially the capacitor is uncharged. What is the steady state charge on it $\left(in\mu C\right)$  after the switch is closed?

In gravity free space, a bead of charge $1\mu C$ and mass 3mg is threaded on a rough rod of friction coefficient $\mu$ = 0.3. A magnetic field of magnitude 0.2 T exists perpendicular to the rod. The bead is projected along the rod with a speed 4m/s. How much distance (in m) will the bead cover before coming to rest?

The new white belt of a long horizontal conveyor is moving with a constant speed v = 3.0m/s. A small block of carbon is placed on the belt with zero initial velocity relative to the ground. The block will slip a bit before moving with the belt, leaving a black mark on the belt (figure). How long is that mark (in m) if the coefficient of kinetic friction between the carbon block and the belt is 0.20 and the coefficient of static friction is 0.30?

A calorimeter consists of 400g of water at $24°C.$ A 500g piece of copper at $100°C$ is thrown into the water and the equilibrium temperature is found to be $36.5°C.$  What is the molar heat capacity of copper in cal/mol k, given that 1 mol of copper has a mass of 63.5g? Neglect the heat capacity of the container.

You are given a converging lens with equal radii of curvature and a diverging lens with the same radii of curvature as those of the converging lens. The lenses are made of material with n = 1.50, the radii of curvature are all 35cm. They are placed at opposite ends of a tube 15cm long, and the nearer lens which is converging is 10cm from an object. What is the location of the image that results from the two refractions? Write the final distance (in cm) from diverging lens.

In the circuit in figure we have ${\epsilon }_1={\epsilon }_2$  = 100V, R₁ = 20 $\Omega$ , R₂ = 10 $\Omega$ , R₃ = 40 $\Omega$  and R₄ = 30 $\Omega$ . Find the reading of the ammeter (in A). Disregard the resistance of the battery and the ammeter.

An electron moves in the field produced by a charged sphere of radius 10cm along the radius connecting the points separated by 12 and 15 cm from the centre of the sphere. The velocity of the electron changes thereby from 2 * 10⁵ to 2 * 10⁶ m/s. Determine the surface charge (in nC/m²) density of the sphere. (Mass of electron = 9.1 * 10^-31kg)

A small elastic ball of mass m is placed at the apex of a $45°$  inclined plane as shown in the figure below. The ball is allowed to slip without friction down the plane (along the dotted line), hit the ground (as shown) and bounce along it. If the height of the inclined plane is h and the coefficient of restitution between the ball and the ground is 0.5, then the distance AB, as marked on the figure, will be N * h, where N is

You are trying to construct a compound microscope given two lenses with focal lengths f₁ = 1.0cm and f₂ = 4.0cm. How far apart (in cm) should you place the lenses in order to obtain an angular magnification of 60? (Assume normal adjustment of microscope)