Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA; while the other through AC, CD and DA (see Fig. 12.12). Then they cleaned the area enclos

Students of a school staged a rally for cleanliness compaign. They walked through the lanes in two groups. One group walked through the lanes A B ,\ B C\ a n d\ C A ; while other through A C ,\ C D\ a n d\ D A (See in Figure). Then they cleaned the area enclosed within their lanes. If A B=9m\ B C=40 m ,\ C D=15 m ,\ D A=28 m ,\ a n d\ /_B=90^0dot Which group cleaned more area and by how much? Find the total area cleaned by the students.

A closed cubical box is made of perfectly insulating material and the only way for heat to enter or leave the box is through two solid cylindrical metal plugs, each of cross sectional area 12cm^(2) and length 8cm fixed in the opposite walls of the box. The outer surface of one plug is kept at a temperature of 100^(@)C . while the outer surface of the plug is maintained at a temperature of 4^(@)C . The thermal conductivity of the material of the plug is 2.0Wm^(-1)C^(-1) . A source of energy generating 13W is enclosed inside the box. Find the equilibrium temperature of the inner surface of the box assuming that it is the same at all points on the inner surface.

Thin films, including soap bubbles and oil show patterns of alternative dark and bright regions resulting from interference among the reflected ligth waves. If two waves are in phase, their crests and troughs will coincide. The interference will be cosntructive and the amlitude of resultant wave will be greater then either of constituent waves. If the two wave are not of phase by half a wavelength (180^(@)) , the crests of one wave will coincide width the troughs of the other wave. The interference will be destructive and the ampliutde of the resultant wave will be less than that of either consituent wave. 1. When incident light I, reaches the surface at point a, some of the ligth is reflected as ray R_(a) and some is refracted following the path ab to the back of the film. 2. At point b, some of the light is refracted out of the film and part is reflected back through the film along path bc. At point c, some of the light is reflected back into the film and part is reflected out of the film as ray R_(c) . R_(a) and R_(c) are parallel. However, R_(c) has travelled the extra distance within the film fo abc. If the angle of incidence is small, then abc is approxmately twice the film's thickness . If R_(a) and R_(c) are in phase, they will undergo constructive interference and the region ac will be bright. If R_(a) and R_(c) are out of phase, they will undergo destructive interference and the region ac will be dark. I. Refraction at an interface never changes the phase of the wave. II. For reflection at the interfere between two media 1 and 2, if n_(1) gt n_(2) , the reflected wave will change phase. If n_(1) lt n_(2) , the reflected wave will not undergo a phase change. For reference, n_(air) = 1.00 . III. If the waves are in phase after reflection at all intensities, then the effects of path length in the film are: Constrictive interference occurs when 2 t = m lambda // n, m = 0, 1,2,3 ,... Destrcutive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n) , m = 0, 1, 2, 3 ,... If the waves are 180^(@) out of the phase after reflection at all interference, then the effects of path length in the film ara: Constructive interference occurs when 2 t = (m + (1)/(2)) (lambda)/(n), m = 0, 1, 2, 3 ,... Destructive interference occurs when 2 t = (m lambda)/(n) , m = 0, 1, 2, 3 ,... The average human eye sees colors with wavelength between 430 nm to 680 nm. For what visible wavelength (s) will a 350 nm thick (n = 1.35) soap film produce maximum destructive interference?

Two heavy metallic plates are joined together at 90^@ to each other. A laminar sheet of mass 30kg is hinged at the line AB joining the two heavy metallic plates. The hinges are frictionless. The moment of inertia of the laminar sheet about an axis parallel to AB and passing through its center of mass is 1.2 kg m^2. Two rubber obstacles P and Q are fixed, one on each metallic plate at a distance 0.5m from the line AB. This distance is chosen so that the reaction due to the hinges on the laminar sheet is zero during the impact. Initially the laminar sheet hits one of the obstacles with an angular velocity 1 rad/s and turns back. If the impulse on the sheet due to each obstacal is 6 N-s, (a) Find the location of the center of mass of the laminar sheet from AB. (b) At what angular velocity does the laminar sheet come back after the first impact? (c) After how many impacts, does the laminar sheet come to rest?