WBUT Exam Papers
Mechanical Science B Tech Ist Sem Dec 2008
Time : 3 Hours ]
Full Marks : 70
GROUPA ( Multiple Choice Type Questions)
 1. Choose the correct alternatives for the following : 10 x 1 – 10
1) Free body diagram can be applied only in
a) dynamic equilibrium problem
b) static equilibrium problem
c) both dynamic and static equilibrium problems
d) none of these. ‘
ii) The conditions of equilibrium for coplanar nonconcurrent forces are a) I F_{x} = 0 ; I F _{Y} = 0 b) I F_{x} * 0 ; I M = 0
c) XF_{y} = 0; XM = 0 d) IF_{X} = 0; lF_{y}=0; IM = 0.
iii) The centre of gravity of solid hemisphere of radius R is a) 3R / 8 , b) R j 2
c) 3R / 4 dj none of these. f 1
iv) Equation of motion of a particle is s = 2t^{3} – t^{2} – 2 where s is displacement in metre and t is time in second. Acceleration of the particle after 1 second will be
a) 8 m/sec^{2} b) 9 m/sec^{2}
c) 10 m/sec^{2} d) 5 m/sec^{2}. 
v) When a body slides down an inclined surface of inclination 0, the acceleration of the body is given by
a) f=g b) /= g sin 0
c) 1=9 cos 0 d) /= g/sin 0.
vi) The maximum strain energy that can be stored in a body is known as
a) impact energy b) resilience
c) proof resilience d) modulus of resilience.
vil) When two ships are moving along inclined directions, then the time when the two ships will be closest together depends upon
a) velocity of one of the ships
b) velocity of both the ships
c) angle between the two directions
d) all of these.
viii) The maximum height of a projectile on a horizontal range is
( u ^{2} sin 2a ) ( u ^{2} sin
a ) 2g ^{b)} 2g
(u^{2} sin^{2} 2a) (u^{2}sin^{2}a)
^{C)} 2cji ^{d)} 2g •
ix) The differential equation of falling body under gravity is
a) x = 0, y = 0 b) x = 0, y = – g
c) x — c, y = – g d) x=0, y= 0
e) none of these.
x) If a momentum of a body is doubled, its kinetic energy will
a) increase by two times b) increase by four times
c) remain same – d) get halved
e) reduce to four times.
GROUP B ( Short Answer Type Questions )
Answer any three of the following.
 2. What do you mean by a Free Body Diagram ? Draw the Free Body Diagrams of the following as shown below :
 3. Determine the force P required to intend the motion of the block B shown In the figure below. Take \i = 03 for all surfaces of contact, where p = coefficient of friction 5
A force = 31 – 4/ + 12k acts at a point A whose coordinates are (1. 2. 3 J n. Compute.
a) moment of force about origin °
b) moment of force about the point B ( 2. 1, 2 ) m.
5. If the string AB is horizontal, find the angle that the string AC makes with th*. horizontal when the ball is in a position of equilibrium. Also find the pressure R between the ball and the plane.
GROUP C ( Long Answer Type Question* )
Answer any three of the following questions.
6 a) A short semicircular right cylinder of radius r and weight W rests on a horizontal surface and is pulled at right angles to its geometric axis by a horizontal force P applied at the middle B of the front edge as shown. Find the angle a that the flat face will make with the horizontal plane just before sliding begins if the coefficient of friction at the line of contact A is p. The gravity force W must be considered as acting at the centre of gravity C as shown in the figure.
•’ b) Determine the coordinates of the centroid C of the area of the circular sector OBD of radius r and central angle a.
7. a) The following details refer to the bar as shown :

If the load P_{4} = 80 kN. P_{2} = 60 kN and P_{3} = 40 kN. find the extension of the bar, where E = 2 x 10 ^{5} N/mm^{2} .
b) Calculate the increase in stress for each segment of the compound bar shown L figure, if the temperature increases by 100°F. Assume that the supports are unyielding and that the bar is suitably braced against buckling. 8
E = 10 x 10“ psi
A – 2.0 in.^{2 }^{E} ~ ^{29} X 10^{6} psi
S. a = 12.8 X l0«/°F ^{A} “15 *”•*
1 ot – 6.5 X 10 ^{a}/°F ^
\ Aluminum I Steel ^ ^—– 1—————————— ^
v “• 10 in. *■ 16 in. ■ S
8. a) A spring normally 150 mm long is connected to the two masses as shown in figure and compressed 50 mm. If the system is released on a smooth horizontal plane, what will be the speed of each block when the spring is again in is normal length ? The spring constant is 2100 N/m. 8
M, – 1.5 k
VW^“
A projectile is aimed at a mark on the horizontal plane through the point of projet tion and falls 12 m short when the angle of projection is 15°. while It overshoots the mark by 24 m when the same angle is 45°. Find the angle of projection to hit the mark. Assume no air resistance. Consider the velocities of
projections are constant in all cases. 7
^{3) Tw}° ^{inclined r}°Hers. each of weight Q = 100 kgf are supported by an inclined plane and a vertical wall as shown below. Assuming smooth surfaces, find the reactions induced at the points A. B and C. _{7}
b) Two blocks of weight W _{l} and W_{2} rest as shown. If the angle of friction of each block is (p. find the magnitude and direction of the least force P applied to the
upper block that will induce sliding.