Physics

A capacitor of capacitance 3µF is charged to a potential difference of 12V. Another identical capacitor, initially uncharged is filled with a dielectric having dielectric constant K and it is connected to the charged capacitor. The final common potential difference across both capacitors is found to be 2V. Find the value of k.

A wooden wheel having radius of 1 m is to be fitted with an iron ring around it. The diameter of the ring is 6 mm smaller than the wooden wheel. If the coefficient of linear expansion of iron is 1.2 * 10^-5/ °C, then find the minimum increase in temperature (in °C) to fit the ring on the wheel.

A bucket of height 20 cm is placed under a tap such that water flows into the bucket at a constant rate of 100 cm³/s. There is a small hole in the bucket of cross-sectional area of 1 cm² at height of 3 cm from the bottom. Area of hole is very small as compared to area of the bucket. Find the maximum height (in cm ) above the bottom upto which the water is filled in the bucket. (Take g = 10 m/s² )

In a young's double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved 8 cm towards the slits, the change in fringe width is 4 * 10^-5 m. If the separation between the slits is 1 mm, find the wavelength of light used (in nm ).

12gm of gas occupy a volume of 4 * 10^-3 m³ at a temperature of 7°C. After the gas is heated at constant pressure its density becomes 6 * 10^-4gm/cm³. What is the temperature to which the gas was heated (in kelvin)?

A fish moving up in water (μ = 4/3) with a speed of 4 cm/s observes a bird coming directly towards itself with a speed of 12 cm/s. Find the actual speed of the bird with respect to a stationary observer on the ground.

A hollow sphere (mass m, radius R) is put inside a hollow cone (mass m, radius 3R and semi-angle $30°$ ) as shown in the figure. The whole arrangement is rigidly fixed to the ground at the apex of the cone. Both the sphere and the cone are made of the same material (a = 10^-4/ $°C$ ). Considering that major changes in dimensions could happen only due to heating effects, find the increase in potential energy (in Joule) of the system if it's temperature is increased by   $100°C.$

An electromagnetic wave is represented by the electric field
E⃗ = E₀n̂[ωt + (y − z)]
The direction of propagation of the wave, ŝ is:

A monochromatic light of wavelength 6500 Å is used in YDSE. Now both slits are covered by two thin slab of refractive index 3.2 and 2.7 respectively. By doing so central bright fringe shifts to original 7^th bright fringe. If both slabs have same thickness then thickness of slab is $\left(in\mu m\right).$  

The rest mass of the deuteron, proton and neutron is equivalent to energy of 1877MeV, 939MeV, 940MeV respectively. A deuteron may disintegrate to a proton and neutron if it.