![Qn2. Supposing that: [period] = [mx] [lg] [gz]. Find the value of: a) (i) X (ii) y (iii) z](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1780475537622-3627a016571e7e0b.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
here's the solution to your question: a) To find the values of x, y, and z, we use dimensional analysis. The dimensions of the quantities are: • Period [T] = [T] • Mass [m] = [M] • Length [l] = [L] • Acceleration due to gravity [g] = [LT^-2] The given relationship is [period] = [m^x][l^y][g^z]. Substituting the dimensions: [T] = [M^x][L^y][(LT^-2)^z] [M^0 L^0 T^1] = [M^x L^y L^z T^-2z] [M^0 L^0 T^1] = [M^x L^y+z T^-2z] Now, we equate the exponents of M, L, and T on both sides: For M: x = 0 For L: y+z = 0 For T: 1 = -2z Step 1: Solve for x. From the exponent of M: x = 0 The value of x is 0. Step 2: Solve for z. From the exponent of T: 1 = -2z z = -(1)/(2) The value of z is -(1)/(2). Step 3: Solve for y. From the exponent of L: y+z = 0 Substitute the value of z: y + (-(1)/(2)) = 0 y = (1)/(2) The value of y is (1)/(2). What's next? Send 'em!