Lecture 2

1. Rectangular coordinate system is also known as

Space coordinate system
Polar coordinate system
Cartesian coordinate system
CPlanar coordinate system

2. The least distance between two points on the equatorial circle on the surface of the earth having polar coordinates (R,0) and (R, /2) with respect to the origin at the centre of the Earth is

R
R/2
R

/2
R

3.The range of azimuthal angle in the spherical polar coordinates is

[0,2

]
[0,

]
[-

, +

]

4. The equation to a surface in spherical coordinates is given by =/3. The surface is

A sector of a circle
A cone making an angle of

/3 with the z-axis
A vertical plane making an angle of

/3 with the x-axis

5. The equation to a surface in spherical coordinates is given by =/3. The surface is

A sector of a circle
A cone making an angle of

/3 with the z-axis
A vertical plane making an angle of

/3 with the x-axis

6. In two dimensions, for the transformation from a pair of variables (x,y) to a new pair (u,v), the Jacobian is

The ratio of the elemental area dudv to the area dxdy
The ratio of the elemental area dxdy to the area dudv
Only depends on the area element dxdy
Only depends on the new area element dudv

7. The Jacobian for transformation from three dimensional Cartesian coordinates to spherical polar coordinates is

8. Expressed in spherical coordinates, the equation becomes