Question

Use dimension m→[M] x→[L] for the variables in the following questions) 1. If a variable K has dimensions 17] v→ a→ MIUY, what should be dimension of k in the equation K - Amv 2. What should be the dimensions of C, and C2 in the expression v Ce? 3. What should be the dimensions of , Aand A, in the expression r AA, sin (o)? 4. The distance d that a particle moves may be calculated from the expression d-at+bt2 where a and b are constants and t is the elapsed time. What are the dimensions of the quantities a and b? 5. A certain physical quantity, R, is calculated using the formula: R- lengths. What is the SI unit for R? What is the standard unit for R? where a, b, and c are 6. The mathematical relationship between three physical quantities is given by a.If the dimension of b isdte dimension of c is L. What is the dimension of a? Use the following figure for questions 7 and 8. Assume that the arrows are drawn to scale 7. Consider two vectors A and B in the top part of the figure above. The difference A-B is represented by which figure? 8. Consider two vectors A and B in the top part of the figure above. The difference B-A is represented by which figure?

Answer 1

K = k mv^2 ML^2/T^2 = K M L^2/T^2 K = M^0 L^0 T^0 V = C_1 e^-C_2 t c_2 times t will be dimension C_2 T = M^0 L^0 T^0 C_2 = T^-1 C_1 and C will have same dimension C_1 = L T^-1 n = A_1 + A_2 sin (w t) wt is angle it will be dimension WT = M^0 L^0 T^0 W = T^-1 sin (w t) is dimension therefore A_1 = A_2 = L