A rod of length L has non-uniform linear mass density (mass per unit length) lambda, which varies as lambda = lambda_0 (S/L), where lambda_0 is a constant and S is the distance from the end marked 'O' (as shown in the figure). Find the centre of mass of the rod.

2Medium10 marks

Which of the following elementary particle reactions/decays are allowed under various conservation laws? If allowed, write down the type of interaction and the characteristic time by which it would proceed:

(i) p -> n + Sigma^+

(ii) pi^- + n -> Lambda^0 + K^-

(iii) p -> n + K^+ + Sigma^-

(iv) pi^+ -> mu^+ + v_mu

(v) pi^0 -> p + e^- + v_e

3Medium10 marks

A star is receding with a speed of 3000 km/s and emitting spectral line of hydrogen, H_alpha of wavelength 656.1 nm. What would be the wavelength observed by an observer on the Earth?

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