Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to:-

A liquid of coefficient of cubical expansion $\gamma$ <!-- [if gte mso 9]><xml> </xml><![endif]--> is filled in a container having coefficient of linear expansion $\frac{\gamma }{3}.$ <!-- [if gte mso 9]><xml> </xml><![endif]--> On heating, liquid level in the container will

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.

Reason R : On heating, the length of the rod increases.

In the light of the above statements, choose the correct answer from the options given below:

At what temperature a gold ring of diameter 6.230cm be heated so that it can be fitted on a wooden bangle of diameter. 6.241cm? Both the diameters have been measured at room temperature (27°C).

(Given : coefficient of linear thermal expansion of gold a_L = 1.4 × 10^-5 K^-1)

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.

An igloo, a hemispherical enclosure built of ice $\left(1.67J/m-s°C\right)$ , has as inner radius of 2.50m. The thickness of the ice is 0.5m. At what rate must thermal energy be generated to maintain the air inside the igloo at $5°C$ when the outside temperature is - $40°C?$  Ignore all thermal energy losses through the ground or by air currents.