Cochin University of Science and Techology (CUST) 2006 B.Tech Civil Engineering Engineering Mechanics - Question Paper
I;
BTS(C) - 1 06 -005 (B)
B. Tech Degree I & II Sem ester (Combined) Examination June 2006
IT/CS/EC/CE/ME/SE/EB/E1 /E E/MRE 105 ENGINEERING MECHANICS
(2000 Admissions onwards)
Time : 3 Hours Maximum Marks: 100
(7)
I.
(a)
(b)
State and prove theorem of Varignon. Neglecting friction, find the angle fi of line AB with horizontal f jr equilibrium and if W, -100.V. W,= 200N.
(10)
S'
OR
State the laws of coulomb riction.
What force F is needed to got the BOON block moving to the right? The coefficient of friction for all contact surface is 0.25.
(5)
(12)
II.
(a)
(b)
r
[ iwr'f
I--------L
1 9oorJ
in.
Determine the centroid of the section in the figure given below. /.Iso determine
Ix Sc I for the axes passi ig through
centroid.
1-1 c
>r
(17)
:r
y
OR
IV.
Locate the centroid of the shaded area shown in the figure. Also determine /r,.
(17)
x ~ y ' xy
| orVT' " *
Determine the axial force in ali the members of the truss shown in the figure.
(16)
Explain the principle of viitual work.
Find the reaction at A,B,C and D for the beam shown in the Igure using principle of virtual work
V
A body of mass 4kg drop; freely from a height of 50m and penetrates into the ground by one metre. Find the average resistance of penetration ant1 the time of penetration.
OR
The acceleration of a particle moving in a straight line is directed towards a fixed point 0 and is inversely proportional to the distance of the p article from 0. At time t 0, the displacement is 0.4m, velocity is 1,4m/s and the acceleration is 0.8m/s2.
Find the velocity when ths: displacement is 0.9m and the displacement when the velocity is zero.
A rotor of an electric motcr is uniformly accelerated to a speed of 1800rpm from rest for 5 seconds and ther immediately power is switched off and the rotor decelerate uniformly. If the total tirm: elapsed from to stop is 12.5sec, ietermine the number of revolutions made in (i) acceleration (ii) deceleration. Also determine the value of deceleration.
OR
A gun of mass 3000kg fires horizontally a shell of mass 50k % with a velocity of 300m/s. What is the velocity with which the gun will recoil? Also determine the uniform force required to stop the gun in 0.6m. In how much time it will stop?
A particle is performing a S.H.M. When it is at distances of 10.0cm and 20.0cm from the mean position its velot ities are 1,2m/s and 0.8m/s respectively.
Find (i) amplitude (ii) time period
(iii) its maximum velocity and (iv) its maximum acceleration.
A cylinder of mass M and radius V resting on an inclined plane is released from rest and rolls down the inclined plane without slipping. Determine
(i) the acceleration of its center of mass
(ii) the maximum angie 0 of the inclined plane for which the body will roll without slipping
(iii) the maximum veloc ty of the center of the cylinder aflerit has roMed a distance of 1 m. Assume the coefficient of static friction fj, = 0.192
OR
Derive the expression for he period of small oscillation of t compound pendulum. Determine the period of small oscillation of the Compound >endulum shown in the figure consisting of a dist of diameter 25.4cm and weight 13.5 or suspended by a slender bar of weight 2.25N and length 30cm.
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