Theory of Machines - Theory of Machine
Exam Duration: 45 Mins Total Questions : 30
In a kinematic chain, a quaternary joint is equivalent to
- (a)
one binary joint
- (b)
two binary joints
- (c)
three binary joints
- (d)
four binary joints
In a four bar linkage, if the lengths of shortest, longest and the other two links denoted by s, I, p and q, then it would result in Grashof's linkage provided that
- (a)
l + p < s + q
- (b)
l + s < p + q
- (c)
l + p > s +q
- (d)
l + p = s + q
Find the degree of freedom of mechanism.
- (a)
0
- (b)
1
- (c)
2
- (d)
3
In the shown mechanism, it is given that
AB = 30 cm, BD = 28 cm
BC = 60 cm, DC = 40 cm and speed of crank AB is 500 rpm then angular velocity of link BC is
- (a)
23 rad/s
- (b)
14.7 rad/s
- (c)
19.6 rad/s
- (d)
None of these
If mechanism forms a structure then the number of degree of freedom (n) is
- (a)
0
- (b)
2
- (c)
1
- (d)
-1
A combination of kinematic pairs, joined in such a way that the relative motion between the links is completely constrained, is called a
- (a)
kinematic chain
- (b)
inversion
- (c)
structure
- (d)
mechanism
The component of the acceleration, parallel to the velocity of the particle, at the given instant is called
- (a)
coriolis component
- (b)
tangential component
- (c)
radial component
- (d)
None of these
A ball P slides on the rod pivoted at point 0 and rotating with angular velocity \(\omega \) = 10 rad/s. If it is moving with velocity 5 m/s along link OC then coriolis component of acceleration is
- (a)
100 m/s2
- (b)
2 m/s2
- (c)
50 m/s2
- (d)
zero
In a crank slider mechanism, crank rotates with angular velocity 20 rad/s.
If length of crank radius is 10 cm, then angular velocity of connecting rod is
- (a)
100 rad/s
- (b)
50 rad/s
- (c)
10 rad/s
- (d)
None of these
In which figure, direction of coriolis component of acceleration shown is correct
- (a)
Fig. (1)
- (b)
Fig. (2)
- (c)
Fig. (3)
- (d)
None of these
If number of instantaneous centres are 6 then number of links are
- (a)
4
- (b)
5
- (c)
6
- (d)
Data is insufficient
In a quick return motion mechanism, length of crank radius is 3 cm and length of fixed end is 5 cm, then the ratio of time of cutting stroke to return stroke is
- (a)
1.2
- (b)
2.38
- (c)
3.7
- (d)
4.2
The natural angular frequency of the system will be
- (a)
\(\sqrt { \frac { 3({ k }_{ 1 }+{ k }_{ 2 }) }{ m } } \)
- (b)
\(\sqrt { \frac { ({ k }_{ 1 }+{ k }_{ 2 }) }{ 3m } } \)
- (c)
\(\sqrt { \left( \frac { { k }_{ 1 }+{ k }_{ 2 } }{ 3m } \right) } \)
- (d)
\(\sqrt { \left( \frac { 3m }{ { k }_{ 1 }+{ k }_{ 2 } } \right) } \)
What will be the natural frequency of the system?
Given, E = 200 N/mm2
- (a)
0.89 x 10-4 Hz
- (b)
1.295 x 10-3 Hz
- (c)
2.94 x 10-3 Hz
- (d)
1 x 10-3 Hz
The value of \(\frac { c\omega }{ s } \) is equal to the
- (a)
\(\frac { c\omega }{ { c }_{ c }{ \omega }_{ n } } \)
- (b)
\(\frac { 2c }{ { c }_{ c } } \times \frac { \omega }{ { \omega }_{ n } } \)
- (c)
\(\sqrt { \frac { 2c }{ { c }_{ c } } \times \frac { \omega }{ { \omega }_{ n } } } \)
- (d)
\(\frac { 2c }{ { c }_{ c } } \sqrt { \frac { \omega }{ { \omega }_{ n } } } \)
\(m\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +c\frac { dx }{ dt } \)sx = 0 shows a vibration system, the angular frequency of vibration system is
- (a)
\(\sqrt { s/m } \)
- (b)
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
- (c)
\(\frac{s}{m}\)
- (d)
\({ \frac { s }{ m } -\left( \frac { c }{ 2m } \right) }^{ 2 }\)
If amplitude of vibration reduces to 0.25 of its initial value after five oscillations. The logarithmic decrement will be
- (a)
0.35
- (b)
0.33
- (c)
0.28
- (d)
0.25
\(3\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +6\frac { dx }{ dt } \)15x = 20 cos 4t shows a vibration system. Maximum amplitude of the system will be
- (a)
50 cm
- (b)
51 cm
- (c)
49 cm
- (d)
52 cm
In vibration isolation system, if\(\frac { \omega }{ { \omega }_{ n } } \)1, then the phase O)n difference between the transmitted force and the disturbing force is
- (a)
90o
- (b)
60o
- (c)
180o
- (d)
270o
In vibration isolation system, if \(\frac { \omega }{ { \omega }_{ n } } \)is less than \(\sqrt{2}\), then n for all values of damping factor, the transmissibility will be
- (a)
equal to unity
- (b)
less than unity
- (c)
-1
- (d)
greater than unity
10\(\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } \)+1000x=0 shows a vibration system. The time period of system is
- (a)
3.14 s
- (b)
0.628 s
- (c)
0.314 s
- (d)
6.28 s
In given figure a disc has mass m and its radius is R. What will be natural frequency of the system?
- (a)
\(\frac { 1 }{ 2\pi } \sqrt { \frac { k }{ m } } \)
- (b)
\(\frac { 1 }{ 3\pi } \sqrt { \frac { k }{ m } } \)
- (c)
\(\frac { 1 }{ \pi } \sqrt { \frac { k }{ m } } \)
- (d)
\(\frac { 2 }{ \pi } \sqrt { \frac { k }{ m } } \)
A rigid body, under the action of external forces, can be replaced by two masses placed at a fixed distance apart. The two masses form an equivalent dynamical system, if
- (a)
centre of gravity of two masses coincides with that of body
- (b)
the sum of two masses is equal to the total mass of the body
- (c)
the sum of mass moment of inertia of the masses about their centre of gravity is equal to the mass moment of inertia of the body
- (d)
All of the above
If I, and 12 are the distances of two masses from the centre of gravity of the body and kG is the radius of gyration of the body, then the essential condition of placing the two masses, so that the system becomes dynamically equivalent is
- (a)
l1l2=\({ k }_{ G }^{ 2 }\)
- (b)
l1l2=\(\sqrt{k_{G}}\)
- (c)
l1=kG
- (d)
l2=kG
The velocity ratio of two pulleys connected by an open belt or crossed belt is
- (a)
directly proportional to their diameters
- (b)
inversely proportional to their diameters
- (c)
inversely proportional to square of their diameter
- (d)
None of the above
The connecting rod of an engine has length 300 mm between its centres. If mass of rod is 70 kg and mass moment of inertia is 7000 kq-rnrn". Centre of gravity is at 100 mm from big end.
For dynamical equivalent system, if one mass is placed at small end then other mass will be placed at
- (a)
1.0 mm
- (b)
1.2 mm
- (c)
0.5 mm
- (d)
0.7 mm
Consider a turning moment diagram of flywheel. The fluctuation of energy is 56 kN-m. For flywheel m = 6500 kg and k = 1.8 m. If average speed of engine is 120 rpm, then maximum and minimum speeds are
- (a)
121, 119
- (b)
101,99
- (c)
127, 111
- (d)
100,98
In the given figure, rope makes 2.5 turns round this drum having diameter 300 mm. The weight w is 9 kN.
What will be the value of F to rotate this drum with 20 rpm?
- (a)
171.21 kN
- (b)
180kN
- (c)
190 kN
- (d)
176.47 kN
A flat belt is 100 mm wide and 10 mm thick with density 1000 kg/m3. The maximum stress in belt is not to exceed 1 MPa. The speed of belt at which it transmits the maximum power is
- (a)
20 m/s
- (b)
22.25 m/s
- (c)
16 m/s
- (d)
18.75 m/s
Consider a crankslider mechanism in which Mass of reciprocating part is 500 kg. Crank moves with 20 rad/s and its length is 0.2 m. Inertia force on reciprocating part when crank has travelled 600 from IDC is (obliquity ratio n = 4)
- (a)
10 kN
- (b)
17 kN
- (c)
12 kN
- (d)
15 kN