13. Assuming no energy dissipation dis in the following simple harmonic oscillation process, vt Be h anoiar what will be the angular frequency of an oscillating object with mass M connected to a uniform spring of mass m and spring force constant k?

14. Total charge Q is distributed uniformly throughout a spherical volume of radius R. Find the electric potential V at a distance r from the sphere center assuming V=0 at infinity. ntial Vat a dists

15.5te The current cofrentdesty density J inside a long sond solid cylindrical wire of radius a is in the direction of the central axis. Its magnitude varies linearly with radial distance r from the axis, J = Jor/a, i.c. J=0atr=0 a 0 and J = Jo atr= r a. Find the magnetic field in all space.

16. Draw the schematic diagram of the Young's interference experiment. State the important noints to carry out such an exnement Derive an nression foethe licht intonsitd points to carry out such an experiment. Derive an expression for the light intensity I at the detection screen as a function of the deviated angle θfrom the central axis, wave length λ and detection screen as a function of the deviated angle from the central axis wave lenoth λ and slit spacing d. The maximum intensity is denoted as Io atθ= 0

(b) Treating the super-nova as an isotropic source, deduce its total emission power and express your result as a multiple of the Sun's luminosity. 

(a) Using the measured photon rate, calculate the radiant power that reaches the face of the telescope objective. 

(b) Calculate the wavelength λE that an observer on Earth would detect for the same signal (in nanometers). (5 points)

(a) Using the Doppler shift between the two spaceships, determine the speed VAB of ship A relative to ship B (express your answer as a fraction of c). (5 points)

16. The figure shows a thin film (in the middle) with different materials on either side: n₁ = 1.40, n2 = 1.50, and n3 = 1.60. We send in a ray of light that is perpendicular to the two parallel surfaces. In air, that light has a wavelength of 800 nm. For some values of thickness L, the reflections to the left undergo fully destructive interference. What is the second smallest value of L that gives that result? Answer in nanometers._____

15. The figure shows a rectangular wire loop lying in three magnetic fields given by these functions (in teslas and seconds): B₁ = 3.00t, B2 = 50.0, B3 = 4.00t²+ 5.00. The dimensions are L₁ = 2.00 m, L2 = 3.00 m, L3 = 1.00 m, and L4 = 2.00 m. The directions of the fields are indicated. The resistance is 5.50 2. What is the current (A) in the circuit at time t = 0.500 s?

14. The first figure shows a closed loop with current i. The loop consists of a half-circle of radius r and a half circle of radius R = 2r. The second figure shows the same half-circles but the small one has been flipped over. The net magnetic field at the common center of the circular sections is B₁ for the first figure and B2 for the second figure. What is the magnitude of the ratio B2 / B1?  

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