Mechanics AD/BE/Mathematics 1 Semester/Term PU — University of the Punjab 2020
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FGSTUDI
FGSTIN UNIVERSITY OF THE PUNJAB
: Roll No.
jate Degree in Arfa/Science & B.A./B.Sc. Part-I Annual Exam-2020 ...
ject: Mathematics B Course-l
Paper: Vector Analysis and Mechanics
Time: 3 Hrs.
Marks: 100
IOTE: Attempt SIX questions in all. selecting ONE question from Section-l, TWO
questions from Section-ll, TWO questions from Section-Ill and ONE question
from Section-IV.
SECTION-.I
2. No. 1. （0）.
a, b, c are the vertices of a triangle, prove that a x b + 8 x c + c x a is
serpendicular to the AABC.
(Il). Show that the four points a, b, c, d are coplanar if
[b c d] - [c a d] + (o 6 d]"[a t c].
2. No. 2. If If u() is unit vector, show thet u. [u + ]+
(H) = 1
8
wW.FGS IIDY com
(il). If r = x i + y/ + zk be a vector function, then show that
div(grad r") = m(m + 1)r"-2.
SECTION-11
Q. No. 3. (1). The resultart of two forces P and Q is of magnitude R. If Q is doubled R is
oubled. If Q is reversed R is again doubled. Show that P2: Q%:R? = 2: 3: 2
IL). Forces P. Q act at a point O and their resultant is R if any transversal
uts the lines of action of the forces in the points A, B, C respectively,
Prove that on + - a
). No. 4 (1). Find the force necessary just to cupport a heavy partiole on an inchic plane of
clination o, where (%>
I).
-o-,,
(i). A herispherical shell rest on rough inclined plane whose angle of friction is
2.
how that the inclination of the plane base to the horizontal cannot be greater than
in-1（2sin2）.u
. No. S
(I). A regular hexagon ABCDEF is composed of six equal heavy uniform rods jointed
gether and two opposite angles C and F are conected by string which is horizontal, AB being
contact with a horizontal plane. A weight W' is placed at the middle point of DE. If W be the
eight of cack rod, show that the tension of the string is
(Ul). A rhombus ABCD is formed of four equa! uniform rods freely jointed together
ad suspended from "A". It is kept in position by a light rod joining the middle points of BC and
D; prove that if "T" be the thrust in this rod and W the weight of the rhombus, then
T = W tan ₫
No. 6
(i). Find the Centre of gravity of uniform lamins forming a quadrant of an ellipse
ounded its semi-axes.
