Physics

Speed of sound in a resonance tube experiment is given by the expression v = 2f₀(l₂ – l₁) where f? is the frequency of the tuning fork and l₁, l₂ are length of the air column. Consider f₀ = 300 Hz with no error in its value. Lengths of the air column l₁ and l₂ are measured as 25.0 cm and 80.0 cm respectively. Find the absolute error in the speed of sound (in m/s).

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 rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each anti-node to be 1mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two case is E₁ and E₂ respectively. Write value of  

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: