Instructions

When liquid medicine of density $$\rho$$ is to be put in theeye, it is done with the help of a dropper. As the bulb onthe topof the dropperis pressed, a drop forms at the opening of the dropper. We wishto estimate the size of the drop. Wefirst assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

Question 51

If $$r = 5 \times 10^{-4} m, p = 10^3 kgm^{-3}, g = 10 ms^{-2}, T = 0.11 Nm^{-1}$$, the radius of the drop when it detaches from the dropper is approximately

Instructions

The key feature of Bohr's theory of spectrumof hydrogen atomis the quantization of angular momentum whenanelectron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.

Question 53

A diatomic molecule has momentof inertia I By Bohr's quantization condition its rotational energy in the $$n^{th}$$ level (n = O is not allowed) is

Question 54

It is found that the excitation frequency from ground to thefirst excited state of rotation for the CO molecule is close to $$\frac{4}{\pi} \times 10^{11}$$ Hz. Then the moment of inertia of

CO molecule about its center of massis close to (Take $$h = 2 \pi \times 10^{-34}$$ J s)

Question 55

In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass = 16 a.m.u.), where 1 a.m.u. $$= \frac{5}{3} \times 10^{-27}$$ kg, is close to

Instructions

For the following questions answer them individually

Question 56

Two transparent media of refractive indices $$\mu_1$$ and $$\mu_2$$ have a solid lens shaped transper material of refractive index $$\mu_2$$ between them as shown in figures in Column II A: traversing these media is also shown in the figures. In Column different relations between $$\mu_1, \mu_2$$ and $$\mu_3$$ are given. Match them to the ray diagrams shown in Column

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Question 57

You are given many resistances, capacitors and inductors. These are connected to variable DC voltage source(the first two circuits) or an AC voltage source of 50 Hz frequency(the next three circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage $$V_1$$ and $$V_2$$. (indicated in circuits) are related as shown in column I. Match the two

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CAT Averages, Ratios & Proportions

CAT Logarithms, Surds & Indices