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(chatquestion)...89 Mechanical Properties of Fluids (a) water rises upto the top of capillary tube and stays there without overflowing A fluid is in streamline flow across a horizont 8. pipe of variable area of cross section. For. which of the following statements is corr (b) water rises upto a point a little below the top and stays there [NEET Ka 13] (a) The velocity is minimum at the na west part of the pipe and the pressure is m mum at the widest part of the pipe (b) The velocity is maximum at the narro part of the pipe and pressure is maximum at the widest part of the pipe (c) Velocity and pressure both are maximum at the narrowest part of the pipe (d) Velocity and pressure both are maximum at the widest part of the pipe water does not rise at all. (c) (d) Water rises upto the tip of capillary tube and then starts overflowing like fountain of radius coaresce to Torm a smgio urop of radius 'R' and volume 'V'. If T' is the surface tension of the liquid, then : [2014] Te is released (a) energy= 4VT Topic 3: Viscosity & Terminal Velocity The terminal velocity v, of a small steel ball of radius r falling under gravity through a column of a viscous liquid of coefficient of viscosity depends on mass of the ball m, acceleration due to gravity g, coefficient of viscosity n and radius r. Which of the following relations is dimensionally correct ?- svr() 9. (b) energy = 3VT is absorbed (e) energy= 3VT is released (d) energy is neither released nor absorbed The wetability of a surface by a liquid depends primarily on (a) surface tension [1992] 12. mgr (a) v, oc (b) v, omgnr [2013] (b) density (c) angle of contact between the surface and the liquid (d) viscosity The angle of contact between pure water and mg nmg (d) v, oc (c) rn 1ension, Dunace Capillarity 10. Water rises to a height 'h' in a capillary tube. If the length of capaillary tube above the surface of water is made less than 'h' then : [2015 RSJ pure glass, is [1996] (a) 0° (b) 45° (c) 90° (d) 135° ANSWER KEY (a) 9

asked Feb 18, 2020 by balaji.thirumalai
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(chatquestion)...Maths lecture.pdf 2. Show that ) (z+1)? = z +2z+1 b) Im(iz) = Re(z) a) Re(z) = - Im(z) 3. Do the following operations and simplify your answer. 1+21 2-1 a) 3-41 5/ C) (1-0* ) 1-0 (2-0 (3-) 51 4. Locate the complex numbers z1+Zz and z-Z2, as vectors where b) z = (-13, 1) . z, = (3,0) a) z, = 21, z, = c) z, = (-3, 1), z, = (1, 4) d) z = a+ ib, z, - a- ib 5. Sketch the following set of points determined by the condition given below: a) | z-1+/-1 b) |z+153 c) |z-4/2 4 61 6. Using properties of conjugate and modulus, show that b) iz =-1Z c) (2+0 = 3- 4/ a) z+3/ = z-3/ 7. Show that (-1+1)' = 8(-1-). 8. Using mathematical induction, show that (whenn - 2, 3, ...) a) z, + z, + ..+ z, = 4 + z, +.+ z, b) z,2, ..Z, = z, Z, ** Z, Show that the equation z- z, Fr which is a circle of radius r centered at z, can be written 9. as | 리-2Re(zz)+|2,1-r. 2.2.6 Argument (Amplitude) of a complex number Definition 2.15 Argument of a complex number z - X+ly is the angle formed by the complex number z - X+ly with the positive x-axis. The argument of a complex number z - x+iy is deonted by argz and is given by arg(z) - tan The particular argument of z that lies in the range -<0Sn is called the principal argument of z and is dented by Argz. Notes:) Argze (-n,7} i) If Os ArgzSA, move counterclock wise direction if not move the other direction 61 Example 2.50: Find the principal argument of the following complex numbers: !!!

asked Feb 17, 2020 by balaji.thirumalai
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