A block of mass `1kg` is tied to a string of length `1m` the other end of which is fixed The block is moved on a smooth horizontal table with constant speed `10ms^(-1)`. Find the tension in the string
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Choose a small element of width `dx` at a distance a from one end of the rod . The mass of the element `dm = (m)/(l) dx` Let `T` is the tension to the rod at a distance x by Newton's second law , from the motion of element of mass `dm` , we have `T - (T + dT) = dm omega^(2) x or - dT = ((m)/(l) dx) omega^(2) x ` Interating above equation we get `- int_(T)^(0) dT = (m omega^(2))/(l) int_(x)^(1) xx dx` `or - |T|_(T)^(0) = (m omega^(2))/(2l)|x^(2) |_(x)^(0)` `or - (0 - T) = (m omega^(2))/(2l)(t^(2) - x^(2))` `or T = (m omega^(2))/(2l)(t^(2) - x^(2))`
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CENGAGE PHYSICS-NEWTON'S LAWS OF MOTION 2-Integer type
