Semester-
1st
N.B.: (1) Question No. 1
is compulsory.
(2) Attempt any THREE
questions from the remaining FIVE questions.
(3) Assume suitable data
if necessary and mention the same clearly.
Q.1 Answer any FIVE questions
a)
The top end of a pole is connected by three cables having tension 500
N, 1500 N and a guy wire ‘AB’ as shown in figure below. Determine tension in
cable ‘AB’ if the resultant of the concurrent force is vertical. [4M]
b)
Locate the centroid of the shaded area obtained by cutting a
semicircle of diameter 20 mm from the quadrant of a circle of radius 20 mm as
shown in Figure. [4M]
c)
A body weighing 1000 N is lying on a horizontal plane. Determine the
necessary force to move the body along the plane if the force is applied at an
angle of 45 degrees to the horizontal with a coefficient of friction 0.24. [4M]
d)
The motion of a particle is defined by the relation x=
+2t+5 where x is the position expressed in meters and time in seconds.
Determine [4M]
(i) Velocity and
acceleration after 5 seconds
(ii) Maximum
or minimum velocity and corresponding displacement.
e)
A steel ball of mass 8 kg is dropped onto a spring of stiffness 600
N/m and
attains
a maximum velocity of 2.5 m/s. Find (i) the height from it is dropped and (ii)
the maximum deflection of spring. [4M]
f)
A ladder AB of length l=4.8 m rests on a horizontal floor at A and
leans against a vertical wall at B. If the lower end A is pulled away from the
wall with a constant velocity 3 m/s, what is the angular velocity of the ladder
at the instant when A is 2.4 m from the wall.[4]
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Q.2 a) Find the resultant of the force system acting on the plate as shown
in Fig. where does this resultant act with respect to point A? [8M]
