Ex/PH/T/IB/8/2013
BACHELOR OF ENGINEERING EXAMINATION, 2013
( 1st Year, 1st Semester )
PHYSICS IB
Time : Three hours Full Marks : 100
Answer any five questions.
1. a) Determine the value of a so that
A = 2ˆi + aˆj +kˆ v and B = 4ˆi - 2ˆj - 2kˆ
are perpendicular to each other.
b) Determine a unit vector perpendicular to the plane of
A = 2iˆ - 6ˆj- 3kˆ v and B = 4ˆi + 3ˆj - kˆ
c) What is meant by gradient of a scalar function ? Show that
Ñj v is a vector perpendicular to the surface given by
j(x,y,z) = C, where C is a constant.
d) Determine the gradient of the scalar field j =1/| r |
where r = xiˆ+ yˆj+ zkˆ. 2+5+1+5+7
2. a) i) What is meant by a conservative vector field ?
ii) Show that a force F v represented by
F = (2xy+ z3 )ˆi + x2ˆj+ 3xz2kˆ v
represents a conservative force.
iii) Find the work done in moving an object in this field from
(1, –2, 1) to (3, 1, 4).