List Of 100 Objective Questions On Applied Mechanics & Graphics Statics
1.A block in the shape of a parallelopiped of sides lm x 2m x 3m lies on the surface. Which of the faces gives maximum stable block ?
1 m x 2 m
2 m x 3 m
1 m x 3m
equally stable on all faces
ANSWER : : 2 m x 3 m
2.A solid sphere of mass M and radius R rolls down a plane inclined at 0 with the horizontal. The acceleration of sphere is
(1/3) g sin0
(2/5) g sin 0
(3/7) g sin 0
(5/7) g sin0
ANSWER : re g is acceleration due to gravity
3.Minimum potential energy of a system will be in the position of
stable equilibrium
unstable equilibrium
neutral equilibrium
all of the above
ANSWER : : stable equilibrium
4.A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. The acceleration of centre of mass of rolling cylinder is
(1/3) g sinB
(2/3) g cos 9
(2/3) g sin 0
g sin 9
ANSWER : re ‘g’ is acceleration due to gravity and 0 is inclination of plane with hori�zontal.
5.A cylinder will slip on an inclined plane of inclination 0 if the coefficient of static friction between plane and cylinder is
less than (1/3) tan 0
less than (2/3) tan 0
less than (1/3) sin 6
less than (2/3) sin 6
ANSWER : : less than (1/3) tan 0
6.When two forces, each equal to P, act at 90� to each other, then the resultant will be
P
PV2
P/V2
2P
ANSWER : : PV2
7.The following is in unstable equilibrium
a uniform solid cone resting on a generator on a smooth horizontal plane
a uniform solid cone resting on its base on a horizontal plane
a solid cube resting on one edge
a satellite encircling the earth
ANSWER : : a solid cube resting on one edge
8.Which of the following represents the state of neutral equilibrium ?
a cube resting on one edge
a smooth cylinder lying on a curved surface
a smooth cylinder lying on a convex surface
none of the above
ANSWER : : none of the above
9.Two circular discs of same weight and thickness are made from metals having different densities. Which disc will have the larger rotational inertia about its central axis ?
disc with larger density
disc with smaller density
both discs will have same rotational inertia
none of the above
ANSWER : : disc with smaller density
10.A rigid body is in a stable equilibrium if the application of any force
can raise the CG of the body but can not lower it
tends to lower the CG of the body
neither raises nor lowers the CG of the body
none of above
ANSWER : : can raise the CG of the body but can not lower it
11.The ratio of the speed of a rolling cylinder to the speed of sliding cylinder is
less than 1
equal to 1
between 1 and 2
greater than 2
ANSWER : : less than 1
12.A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first ?
sphere with greater rotational energy at bottom than cylinder
sphere with lesser rotational energy at bottom than cylinder
cylinder with greater rotational energy at bottom than sphere
both reach the bottom simultaneously with equal rotational energy at bottom
ANSWER : : sphere with lesser rotational energy at bottom than cylinder
13.A uniform pyramid and a uniform prism of same height lie with their base on the surface. Which is more stable ?
pyramid
prism
both equally stable
none of the above
ANSWER : : pyramid
14.A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 2 kg m2 and its rate of rotation 2 revolutions/see. The angular momentum of the body in kg-m2/sec is
4
6 7i
8TC
8
ANSWER : : 8TC
16.The torque produced by a force depends on i) the magnitude of the force ii) the direction of the force iii) the’point of application of the force relative to origin The correct answer is
only (i)
both (i) and (ii)
both (i) and (iii)
all (i), (ii) and (iii)
ANSWER : : all (i), (ii) and (iii)
17.A rod AB carries three loads of 30 N, 70 N and 100 N at distances of 20 mm, 90 mm and 150 mm respectively from A. Neglecting the weight of the rod, the point at which the rod will balance is
109.5 mm from A
119.5 mm from A
125.5 mm from A
132.5 mm from A
ANSWER : : 109.5 mm from A
18.If the resultant of two forces has the same magnitude as either of the force, then the angle between the two forces is
30
45
60
120
ANSWER : : 120
19.The angular speed of a car while taking a circular turn of radius 100m at 36 km/hour, is
0.1 radian/sec
1 radian/sec
100 radian/sec
1000 radian/sec
ANSWER : : 0.1 radian/sec
20.A hoop of radius 3 m weighs 100 kg. It rolls along a horizontal floor so that at its centre of mass has a speed of 200 mm/sec, . The work required to stop the hoop is
2 J
4 J
6 J
8 J
ANSWER : : 4 J
21.Rate of change of angular momentum is equal to
force
torque
linear momentum
impulse
ANSWER : : torque
22.A cube on a smooth horizontal surface
cannot be in stable equilibrium
cannot be in neutral equilibrium
cannot be in unstable equilibrium
can be in any of these states
ANSWER : : can be in any of these states
23.The resultant of two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then,
P = R
Q = R
P = Q
None of the above is correct
ANSWER : : Q = R
24.The total kinetic energy of a hoop of mass 2 kg and radius 4 m sliding with linear velocity 8 m/sec and angular velocity 5 radian/sec is
64 J
400 J
464 J
89 J
ANSWER : : 464 J
25.When a circular wheel rolls on a straight track, then the shape of body centrode and space centrode respectively are
straight line and parabola
straight line and circle
circle and straight line
circle and parabola
ANSWER : : circle and straight line
26.If A is the amplitude of particle executing simple harmonic motion, then the total energy E of the particle is
proportional to A
proportional to A2
proportional to 1/A2
independent of A
ANSWER : : proportional to A2
28.A flywheel of moment of inertia 20 kg-m” is acted upon by a tangential force of 5 N at 2 m from its axis, for 3 seconds. The increase in angular velocity in radian persecond is
1/2
3/2 ‘
2
3
ANSWER : : 3/2 ‘
29.A stone is thrown vertically upwards with a vertical velocity of 49 m/sec. It returns to the ground in
5 sec
8 sec
10 sec
20 sec
ANSWER : : 10 sec
30.The maximum displacement of a particle executing S.H.M. corresponds to
zero potential energy and maximum kinetic energy
zero kinetic energy and maximum potential energy
maximum kinetic energy and maxi-mum potential energy
minimum kinetic energy and minimum potential energy
ANSWER : : zero kinetic energy and maximum potential energy
31.In a simple harmonic motion, the position of equilibrium is always
stable
unstable
neutral
none of the above
ANSWER : : stable
32.A particle moves in a straight line and its position is defined by the equation x = 6 t2 – t3 where t is expressed in seconds and x in metres. The maximum velocity during the motion is
6 m/sec
12 m/sec
24 m/sec
48 m/sec
ANSWER : : 12 m/sec
33.A 2 m long ladder rests against a wall and makes an angle of 30� with the horizontal floor. Where will be the instantaneous centre of rotation when the ladder starts slipping ? i) 1.0 in from the wall ii) 1.732 m from the wall iii) 1.0 m above the floor iv) 1.732 m above the floor The correct answer is
(i) and (iii)
(i) and (iv)
(ii) and (iii)
(ii) and (iv)
ANSWER : : (ii) and (iv)
34.A particle of mass 2 kg executes simple harmonic motion of frequency 6/71 Hz and amplitude 0.25 m. Its maximum kinetic energy is
4.5 J
9.0 J
12.0 J
18.0 J
ANSWER : : 9.0 J
35.If the direction of projection bisects the angle between the vertical and the inclined plane, then the range of projectile on the inclined plane is
zero
maximum
minimum
unpredictable
ANSWER : : maximum
36.It is observed that in a certain sinusoidal oscillation, the amplitude is linearly dependent on the frequency f. If the maximum velocity during the oscillation is V, then V must be proportional to
f
1/f
1/f2
f2
ANSWER : : f2
37.The time period of a simple pendulum depends on i) mass of suspended particle ii) length of the pendulum iii) acceleration due to gravity The correct answer is
only (i)
both (ii) and (iii)
both (i) and (iii)
all are correct
ANSWER : : both (ii) and (iii)
38.Instantaneous centre is at infinity when the angular velocity is
constant
zero
maximum
minimum
ANSWER : : zero
39.At the instantaneous centre, the velocity of the moving lamina at any instant is
zero
maximum
minimum
varying
ANSWER : : zero
40.The maximum value of the horizontal range for a projectile projected with a velocity of 98 m/sec is
98 m
490 m
980 m
1960m
ANSWER : : 980 m
41.A projectile has maximum range of 40 m on a horizontal plane. If angle of projection is a and the time of flight is 1 second, then sin a must be about
1/4
1/3
1/2
1/5
ANSWER : ume g = 10 m/sec2
43.A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is
n rpm
n/2 rpm
n/4 rpm
2n rpm
ANSWER : : n/2 rpm
44.Select the correct statement
The body centrode rolls on the space centrode.
The space centrode rolls on the body centrode.
Both body and space centrodes may role on each other.
The body centrode never touches space centrode.
ANSWER : : The body centrode rolls on the space centrode.
45.A disc of mass 4 kg, radius 0.5m and moment of inertia 3 kg-m2 rolls on a horizontal surface so that its centre moves with speed 5 m/see. Kinetic energy of the disc is
50 J
150 J
200 J
400 J
ANSWER : : 200 J
46.If a projectile is fired with an initial velocity of 10 m/sec at an angle of 60� to the horizontal, its horizontal and vertical velocity at the highest point of trajectory are
0 and 5 m/sec
5 m/sec and 0
5 V3 m/sec and 0
5 and 5V3 m/sec
ANSWER : : 5 m/sec and 0
47.The angle of projection at which the horizontal range and maximum height of a projectile are equal to
45
tan-1 (2)
tan-‘ (4)
tan”1 (1/4)
ANSWER : : tan-‘ (4)
48.A heavy ladder resting on floor and against a vertical wall may not be in equilibrium if
floor is smooth and wall is rough
floor is rough and wall is rough
both floor and wall are rough
both floor and wall are smooth
ANSWER : : both floor and wall are smooth
49.The dimensions of power are.
M’L2T2
M’L’T3
M’L’r2
M’L-‘T*
ANSWER : : M’L’T3
50.Williot-Mohr diagram is used to determine deflection in
trusses only
beam only
rigid frames only
any type of structure
ANSWER : : trusses only
51.If the kinetic energy and potential energy of a simple harmonic oscillator of amplitude A are both equal to half the total energy, then the displacement is equal to
A
A/2
A/V2
AV2
ANSWER : : A/V2
51.One Newton is equivalent to
105 dyne
106 dyne.
107 dyne
981 dyne
ANSWER : s: a
52.One Joule is equivalent to
9.81 Newton – metre
1 Newton – metre
1 kg wt – metre
1 dyne – metre
ANSWER : : 1 Newton – metre
53.A quantity whose dimensions are M2L2 T3 could be the product of
force and pressure
mass and power
energy and velocity
force and velocity
ANSWER : : mass and power
54.Which of the following is a scalar quantity?
energy
momentum
torque
impulse
ANSWER : : energy
55.Time period and length of a seconds pendulum respectively are
1 sec and 99.4 cm
1 sec and 92.7 cm
2 sec and 99.4 cm
2 sec and 92.7 cm
ANSWER : : 2 sec and 99.4 cm
56.A particle is executing simple harmonic motion in a line 1.0 m long. If the time of one complete vibration is 1 sec, then the maximum velocity of the particle is
1.00 m/sec
1.57 m/sec
3.14 m/sec
6.28 m/sec
ANSWER : : 3.14 m/sec
57.Joule is the unit of
power
impulse
work
momentum
ANSWER : : work
58.The dimensions of centrifugal force are
M1 L2 T2
M’L’T1
M’L’T2
M’L-‘T2
ANSWER : : M’L’T2
59.A simple pendulum of length / has an energy E, when its amplitude is A. If the length of pendulum is doubled, the energy will be
E
E/2
2E
4E
ANSWER : : E/2
60.The ratio of unit of force in gravitational system to that in absolute system is
1
g
1/g
none of the above
ANSWER : re ‘g’ is acceleration due to gravity
61.The dimensions of Gravitational Universal constant ‘G’ are
M-‘L2r2
M-‘L3r2
M-2L3T2
M’L3T2
ANSWER : : M-‘L3r2
62.Coefficient of friction depends on
nature of surfaces only
area of contact only
both (a) and (b)
none of the above
ANSWER : : nature of surfaces only
63.The unit of rotational inertia of a body in C.G.S system is
cm4
kg-cm2
gm-cm2
gm-cm3
ANSWER : : gm-cm2
64.One end of an elastic string of natural length / and modulus X is kept fixed while to the other end is attached a particle of mass m which is hanging freely under gravity. The particle is pulled down vertically through a distance x, held at rest and then released. The motion is
a simple harmonic motion
a rectilinear motion with constant speed
a damped oscillatory motion
none of the above
ANSWER : : a simple harmonic motion
65.The ratio of kinetic energy and potential energy of a simple harmonic oscillator, at a displacement equal to half its amplitude is given by
1:2
1:1
2:1
3:1
ANSWER : : 3:1
66.In SI units, the units of force and energy are respectively
Newton and watt
Dyne and erg
Newton and joule
kg-wt and joule
ANSWER : : Newton and joule
67.Impulse can be obtained from a
force-displacement diagram
force-time diagram
velocity-time diagram
velocity-displacement diagram
ANSWER : : force-time diagram
68.A quantity measured in the C.G.S system of units has dimensions M”2L3 T3/2. What numerical factor would be required to convert the quantity to SI units ?
1
100
1/100
1/10000
ANSWER : : 1
69.A rope is wrapped twice around a rough pole with a coefficient of friction ‘A . It is subjected to a force F1 at one end and a gradually increasing force F2 is applied at the other end till the rope just starts slip-ping. At this instant the ratio of F2 to Fi is
1
e2*
e4*
e*72
ANSWER : : e2*
70.One Newton is equivalent to
1 kg-wt
9.81 kg-wt
981 dyne
1/9.81 kg-wt
ANSWER : : 1/9.81 kg-wt
71.The potential energy of a particle falling through a straight shaft drilled through the earth (assumed homogenous and spherical) is proportional to
log r
r
r2
1/r
ANSWER : re r is the distance of’the particle from centre of the earth
72.A particle is dropped from a height of 3 m on a horizontal floor, which has a coefficient of restitution with the ball of 1/2. The height to which the ball will rebound after striking the floor is
0.5 m
0.75 m
1.0 m
1.5 m
ANSWER : : 0.75 m
73.A ball is dropped from a height of 16 m on a horizontal floor. If it rebounds to a height of 9 m after striking the floor, the coefficient of restitution between ball and floor is
1/4
2/3
3/4
4/3
ANSWER : : 3/4
74.Intrinisic equation of catenary is given by
S = C tan q>
S = C cos cp
S = C sin cp
S = C cot
ANSWER : re C is some constant.
75.When a body slides down an inclined surface, the acceleration of the body is given by
g
gsinG
g cos 6
g tan 6
ANSWER : re ‘g’ is acceleration due to gravity and 9 is the angle of inclination of surface with the horizontal.
76.A bullet weighing 10 gm moves with a velocity of lkm/sec. Its kinetic energy is i) 5000 N.m ii) 5000 kg.m iii) 5000 J The correct answer is
only (ii)
both (i) and (iii)
both (ii) and (iii)
all (i), (ii) and (iii)
ANSWER : : both (i) and (iii)
77.In a lifting machine a weight of 5 kN is lifted through 200 mm by an effort of 0.1 kN moving through 15 m. The mechanical advantage and velocity ratio of the machine are respectively
50 and 75
75 and 50
75 and 75
50 and 50
ANSWER : : 50 and 75
78.A body is dropped from a height of 100 m and at the same time another body is projected vertically upward with a velocity of 10 m/sec. The two particles will
never meet
meet after 1 sec
meet after 5 sec
meet after 10 sec
ANSWER : : meet after 10 sec
79.Two objects moving with uniform speeds are 5 m apart after 1 second when they move towards each other and are 1 m apart when they move in the same direction. The speeds of the objects are
2 m/sec and 2 m/sec
3 m/sec and 2 m/sec
3 m/sec and 3 m/sec
4 m/sec and 6 m/sec
ANSWER : : 3 m/sec and 2 m/sec
80.A ball moving on a smooth horizontal table hits a rough vertical wall, the coefficient of restitution between ball and wall being 1/3. The ball rebounds at the same angle. The fraction of its kinetic energy lost is
1/3
2/3
1/9
8/9
ANSWER : : 8/9
81.The angular speed of a car taking a circular turn of radius 100 m at 36 km/hr will be
0.1 rad/sec
1 rad/sec
10 rad/sec
100 rad/sec
ANSWER : : 0.1 rad/sec
82.A car goes round a curve of radius 100 m at 25 m/sec. The angle to the horizontal at which the road must be banked to prevent sideways friction on the car wheels is tan”1 x, where x is (Assume g = 10 m/sec2)
3/8
1/2
9/5
5/8
ANSWER : : 5/8
83.The shape of a suspended cable for a uniformly distributed load over it is
circular
parabolic
catenary
cubic parabola
ANSWER : : parabolic
84.A shell travelling with a horizontal velocity of 100 m/sec explodes and splits into two parts, one of mass 10 kg and the other of 15 kg. The 15 kg mass drops vertically downward with initial velocity of 100 m/sec and the 10 kg mass begins to travel at an angle to the horizontal of tan”1 x, where x is
3/4
4/5
5/3
3/5
ANSWER : : 3/5
85.The maximum pull in a cable, carrying a uniformly distributed load and supported at two ends which are at the same level, is at
supports
quarter span
mid span
none of the above
ANSWER : : supports
86.Minimum pull in a suspended cable with supports at two ends is equal to
horizontal thrust
support reactions
resultant of horizontal thrust and support reaction
half the weight of the cable
ANSWER : : horizontal thrust
87.If a body is lying on a plane whose in-clination with the horizontal is less than the angle of friction, then i) a force is required to move the body upwards ii) a force is required to move the body downward iii) the body will not be in equilibrium The correct answer is
only (i)
only (ii)
both (i) and (ii)
both (i) and (iii)
ANSWER : : both (i) and (ii)
88.Two balls of masses 3 kg and 6 kg are moving with velocities of 4 m/sec and 1 m/sec respectively, towards each other along the line of their centres. After impact the 3 kg ball comes to rest. This can happen only if the coefficient of restitution between the balls is
2/3
1/5
3/5
1/3
ANSWER : : 1/5
89.A stone was thrown vertically upwards from the ground with a velocity of 50 m/sec. After 5 seconds another stone was thrown vertically upwards from the same place. If both the stones strike the ground at the same time, then the velocity with which the second stone was thrown should be (Assume g = 10 m/sec2)
15 m/sec
25 m/sec
40 m/sec
50 m/sec
ANSWER : : 25 m/sec
90.A light rope is loaded with many equal weights at equal horizontal intervals. The points of suspension on the rope lie on a
parabola
catenary
cycloid
ellipse
ANSWER : : parabola
91.Cartesian form of the equation of catenary is
y = c cosh x/c
y = c sinh x/c
y = c tan x/c
y = c sin”1 x/c
ANSWER : : y = c cosh x/c
92.The condilion for a lifting machine to be reversible is that its efficiency should be
less than 50%
more than 50%
more than 66.67%
equal to 100%
ANSWER : : more than 50%
93.A cable loaded with 10 kN/m of span is stretched between supports in the same horizontal line 100 m apart. If the central dip is 10 m, then the maximum and minimum pull in the cable respectively are
1346.3 kN and 1500 kN
1436.2 kN and 1250 kN
1346.3 kN and 1250 kN
1436.2 kN and 1500 kN
ANSWER : : 1346.3 kN and 1250 kN
94.A shell of mass 100 kg travelling with a velocity of 10 m/sec breaks into two equal pieces during an explosion which provides an extra kinetic energy of 20000 Joules. If the pieces continue to move in the same direction as before, then the speed of the faster one must be
20 m/sec
30 m/sec
40 m/sec
50 m/sec
ANSWER : : 30 m/sec
95.If a flywheel increases its speed from 10 rpm to 20 rpm in 10 seconds, then its angular acceleration is
3.14 rad/sec 10
3.14 rad/sec 20
3.14 rad/sec 30
none of the above
ANSWER : : 3.14 rad/sec 30
96.The member forces in a statically in determinate truss
can be obtained by graphic statics
cannot be obtained by graphic statics
may be obtained by graphic statics
can be obtained by graphic statics by trial and error
ANSWER : : cannot be obtained by graphic statics
97.The pole distance is measured in
distance scale
force scale
mass scale
time scale
ANSWER : : force scale
98.Free body diagram is an
isolated joint with only body forces acting on it
isolated joint with internal forces acting on it
isolated joint with all the forces, internal as well as external, acting on it
none of the above
ANSWER : : isolated joint with all the forces, internal as well as external, acting on it
99.The bending moment in an arch is proportional to
vertical ordinate of funicular polygon
vertical ordinate of the arch
intercept between the arch axis and the funicular polygon
none of these
ANSWER : : intercept between the arch axis and the funicular polygon
100.A funicular polygon cannot be made to pass through
one specified point
two specified points
three specified points
more than three specified points
ANSWER : : more than three specified points
101.If a set of given forces are such that their free vectors build a closed polygon, then
the resultant force and resultant couple are always zero
the resultant force is zero but resultant couple is not zero
the resultant force is zero but resultant couple may not be zero
the resultant force and resultant couple both may not be zero
ANSWER : : the resultant force is zero but resultant couple may not be zero
102.In which of the following trusses, the method of substitution is required for determining the forces in all the members of the truss by graphic statics ?
howe truss
king post truss
fink truss
warren truss
ANSWER : : fink truss
103.The force polygon representing a set of forces in equilibrium is a
triangle
open polygon
closed polygon
parallelogram
ANSWER : : closed polygon
104.The number of funicular polygons which can be drawn to pass through two specified points in the space diagram are
zero
1
2
infinity
ANSWER : : infinity
105.A system of copianar forces is in equilibrium when
force polygon closes
funicular polygon closes
both force polygon” and funicular polygon close
all the forces are concurrent
ANSWER : : both force polygon” and funicular polygon close
106.A system of copianar forces acting on a rigid body can be reduced to
one force only
one couple only
one force and one couple only
none of the above
ANSWER : : one force and one couple only
107.Force polygon method is applicable for
any copianar force system
a system of parallel forces only
concurrent copianar force system
non-concurrent copianar force system
ANSWER : : concurrent copianar force system
108.If the given forces P,, P2, P3 and P4 are such that the force polygon does not close, then the system will
be in equilibrium
always reduce to a resultant force
always reduce to a couple
both (a) and (c)
ANSWER : : always reduce to a resultant force
109.If two forces are in equilibrium, then the forces must i) be equal in magnitude ii) be opposite in sense iii) act along the same line The correct answer is
(i) and (ii)
(i) and (iii)
only (i)
(i), (ii) and (iii)
ANSWER : : (i), (ii) and (iii)
110.For a non-concurrent force system to be in equilibrium
only the closure of force polygon is sufficient
only the closure of funicular polygon is sufficient
both force polygon and funicular polygon must close
none of the above
ANSWER : : both force polygon and funicular polygon must close
111.The diagram showing the point of application and line of action of forces in their plane is called
vector diagram
space diagram
force diagram
funicular diagram
ANSWER : : space diagram
112.The condition of equilibrium for any system of forces in a plane is
that polygon of forces must close
that resultant couple must be zero
both (a) and (b)
none of the above
ANSWER : : both (a) and (b)
113.The graphical method of determining the forces in the members of a truss is based on
method of joint
method of section
either method
none of the two methods
ANSWER : : method of joint
114.An ordinate in a funicular polygon represents
shear force
resultant force
bending moment
equilibrium
ANSWER : : bending moment