Q16// Solve the partial differential equation coty given that = =x when y= and u=y when x=0 дхду dx

6

MMP-I

QUESTION 8 Calculate Curl D at the point specified if D=10xyz i+ 5x²zj + (2z³ - 5x²y) k, at P(-2,3,5).

Question 1 A ssuming that the earth is a homogeneous spherical body with radius R, show that its mean density 3g p = 4nGR Question 2

1. Consider the data sets below, determine if it is reasonable to assume that y is proportional to z. If it is, approximate the constant of proportionality. If it is not, describe why this assumption is not reasonable. 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1. 1.2 1.44 1.69 1.96 2.25 2.56 2.89 2. Use dimensional analysis to derive an expression for the volume flow rate, q, in terms of r (the radius of the pipe), u (the viscosity of the fluid) and (the fall in pressure per unit length) dz dp LT L ML-T ML-T %23 19°C A O C

the Volume is equal to Zexo ,then the all Ve ctors line in the Same Plane. a.T b.F

4

Ignore pencil work

Polnts out of 10.00 P Rag question 5x2 522 Let f(x, y, z) = 5y If the level surface 2 f(x, y, z) = 5 has the surface area element of the form do = B(x, y, z)dædz, then evaluate B(2/5,21,2/5). O A. 7.5574 O B. -8.5826 O C. 6.4031 O D. 5.5678 O E. 4.5826 O F. 3.4031 O G. 6.0828 O H. -4.5826