Mechanics Question Paper 2
Exam Duration: 45 Mins Total Questions : 30
An elastic bar of length L area of cross-section A, self weight w is having vertically. It is subjected to an axial compressive load of w units at the bottom end.The change in length of bar is
- (a)
\(\frac { wL }{ 2AE } \left( extension \right) \)
- (b)
\(\frac { 3wL }{ 2AE } \left( extension \right) \)
- (c)
\(\frac { wL }{ 2AE } \left( contraction \right) \)
- (d)
\(\frac { wL }{ AE } \left( contraction\right) \)
A shaft PQRS is subjected to torques at P,Q,R and S as shown in figure. The maximum torque for shaft section occurs between
- (a)
P and Q
- (b)
P and R
- (c)
Q and R
- (d)
R and S
A simply supported beam of rectangular cross-section supports a point load at its mid-point. If the width of the section is doubled, then the maximum deflection in the beam will be N times the deflection of the original beam, where the value of N is
- (a)
0.5
- (b)
1
- (c)
2
- (d)
3
A cantilever carries a total udl of \(\omega \) over its entire length and a force \(\omega \) acts at its free end upwards. The net deflection at the free end is
- (a)
zero
- (b)
\(\frac { 5wL^{ 3 } }{ 24EI } (up)\)
- (c)
\(\frac { 5wL^{ 3 } }{ 24EI } (up)\)
- (d)
\(\frac { wL^{ 3 } }{ 24EI } (up)\)
The principal stress at a point in a strained material are \({ P }_{ 1 }\)and \({ P }_{ 2 }\). The resultant stress \({ P }_{ r }\)on the plane carrying the maximum shear stress would be
- (a)
\(\frac { \sqrt { \left( { p }_{ 1 }^{ 2 }+{ p }_{ 2 }^{ 2 } \right) } }{ 2 } \)
- (b)
\(\sqrt { \left( \frac { { P }_{ 1 }^{ 2 }+{ P }_{ 2 }^{ 2 } }{ 2 } \right) } \)
- (c)
\(\sqrt { 2\left( { P }_{ 1 }^{ 2 }+{ P }_{ 2 }^{ 2 } \right) } \)
- (d)
\(2\sqrt { \left( { P }_{ 1 }^{ 2 }+{ P }_{ 2 }^{ 2 } \right) } \)
A hollow circular column of internal diameter d and external diameter 1.5d is subjected to compressive load. The maximum distance of the point of application of load from the centre for no tension is
- (a)
d/8
- (b)
13d/48
- (c)
d/4
- (d)
13d/96
Four vertical columns of the same material height and weight have the same end conditions. The buckling load will be largest for a column having the cross-section of a/an
- (a)
solid square
- (b)
thin hollow circle
- (c)
solid circle
- (d)
I-section
A cantilevered type gate hinged at Q as shown in figure P and R are the centres of gravity of the cantilever part and the counter weight respectively. The mass of the cantilever part is 75 kg. The mass of the counter weight for static balance , is
- (a)
75 kg
- (b)
150 kg
- (c)
225 kg
- (d)
300 kg
A steel rod of length and diameter d fixed at both ends, is uniformly heated to a temperature rise of \(\triangle T\) .The thermal stress in the rod is
- (a)
zero
- (b)
\(\alpha \triangle T\)
- (c)
\(E\alpha \triangle T\)
- (d)
\(E\alpha \triangle TL\)
The major and minor principle stresses at a point are 3 MPa and -3MPa respectively. The maximum shear stress at the point is
- (a)
zero
- (b)
3 MPa
- (c)
6 MPa
- (d)
9 MPa
Two identical circular rods of same diametre and same length are subjected to same magnitude of axial tensile force. One of the rods is made steel having modulus of elasiticity 206 GPa. The other rod is made of cast having the modulus of elasticity of 100 GPa. Assume the axial force cause the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit, which of the following observations is correct?
- (a)
Both rods elongate by the same amount
- (b)
Mild rod elongate more than the cast iron rod
- (c)
Cast iron elongate more than the mild steel rod
- (d)
As the stresses are equal, strain are equal in both the rods
The ratio of strength of n loose beam (b x d) placed one over other to the strength of one integral beam (b x nd) is,
- (a)
n2
- (b)
n
- (c)
\(\frac { 1 }{ n }\)
- (d)
\(\frac { 1 }{ { n }^{ 2 } }\)
Two simply supported beams B1 and B2 have spans L and 2L, respectively. Beam B1 has a cross-section of 1 x 1 units and beam B2 has a cross-section of 2 x 2 units. These beams are subjected to concentrated loads w each at the center of their spans. The ratio of the maximum flexural stress in the beam is
- (a)
4
- (b)
2
- (c)
\(\frac { 1 }{ 2 }\)
- (d)
\(\frac { 1 }{ 4 }\)
A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length on half of the span from one end. The length of the span and the flexural stiffness are denoted as L and EI respectively. The deflection at the mid span of the beam is
- (a)
\(\frac { 5 }{ 6144 } \frac { wL^{ 4 } }{ EI } \)
- (b)
\(\frac { 5 }{ 384 } \frac { wL^{ 4 } }{ EI } \)
- (c)
\(\frac { 5 }{ 768 } \frac { wL^{ 4 } }{ EI } \)
- (d)
\(\frac { 5 }{ 192 } \frac { wL^{ 4 } }{ EI } \)
In the bending moment diagram for shimply supported beanm is of the form given below, then the load acting on the beam is
- (a)
a concentrated load at C
- (b)
equal and opposite moments at A and B
- (c)
a udl distributed load over the beam
- (d)
a moment applied at C
Two people weighing w each are sitting on length L flloating on water at \( \frac{L}{4}\) from either end.neglecting the weight of plank .The bending moment at the centre of the plank is
- (a)
\(\frac{wL}{8}\)
- (b)
\(\frac{wL}{16} \)
- (c)
\(\frac{wL}{32} \)
- (d)
zero
In which of the following the centroid lies outside the section?
- (a)
Symmetrical I-section
- (b)
tee-section
- (c)
Unsymmetrical section
- (d)
Angle section
What is the diameter of Mohr's circle of stress for the state of stress shown below?
- (a)
zero
- (b)
\(\sigma \)
- (c)
\(\sqrt [ \sigma ]{ 2 } \)
- (d)
\(2\sigma \)
The plane of maximum shear stress has normal stress that is
- (a)
maximum
- (b)
minimum
- (c)
zero
- (d)
None of the above
Pick the incorrect statement from the following four statements.
- (a)
On the plane which carries maximum normal stress, the shear stress is zero
- (b)
Principal planes are mutually orthogonal
- (c)
On the palne which carries maximum shear stress, the normal stress is zero
- (d)
Principal planes are inclined at 450 with plane of maximum shear stress
A simply supported beam as shown in the figure. The resultant reaction at B is equal to
- (a)
2kN (up)
- (b)
2 kN (down)
- (c)
2\(\sqrt{2}\) kN (up)
- (d)
2\(\sqrt{2}\) kN (inclined)
A shaft subjected to obtain experience a pure shear stress on the surface. The maximum principal stress on the surface which is at 450 to the will have a value
- (a)
\(\tau cos45^{ 0 }\)
- (b)
\(2\tau cos45^{ 0 }\)
- (c)
\(\tau cos^{ 2 }45^{ 0 }\)
- (d)
\(2\tau cos45^{ 0 }sin45^{ 0 }\)
A long constriuction member of uniform section is to be liftes using ropes at C and D as shown in figure.This cause banding moments due to self weight as shown .To minimize th epeak value of bending moment , the overhang b shall be such that
- (a)
M2 = 0
- (b)
M1 =M2
- (c)
b = \(\frac{L}{2}\)
- (d)
b = \(\frac{L}{4}\)
An I section beam made of steel has an overall depth of 80 cm, if the developed flange-stress at top and bottom of beam are 4200 kg/cm2 and 1600 kg/cm2 respectively.Then, the depth of neutral axis from the top of beam would be
- (a)
22.07 cm
- (b)
44.14 cm
- (c)
57.93 cm
- (d)
67.13 cm
A beam with th ecross -section given below is subjected to a positive bending moment (causing compression at the top) of 16 kN-m acting around the horizontal axis.The tensile force acting on ther hatched area of the cross section is
- (a)
zero
- (b)
59 kN
- (c)
8.9 kN 17.8 kN
- (d)
17.8 kN
A cylinder water tank 6 m in diameter with its axis vertical is made from steel plates of 3 mm thickness. If circumferential stress is limited to 60 MPa, then
Maximum water pressure inside the tank is
- (a)
70 kN/m2
- (b)
50 kN/m2
- (c)
60 kN/m2
- (d)
100 kN/m2
At a point in a piece of streessed material the stresses are \( \sigma_x \) = \( \alpha\) kN/m2 tensile (Normal ) \(\tau_{xy} \) = \(\tau_{yx}\) = \(\beta\) kN/m2 (shearing ) , although th evalues of \( \alpha\) and \(\beta\) are not known, yet the principal stresse are equal to each other being (5 kN/m2).What is the radius of Mohr's circle?
- (a)
2.5 + \((\alpha+\beta)\)
- (b)
2.5 + \((\frac{\alpha+\beta}{2})\)
- (c)
2.5
- (d)
zero
The figure shows the state of stress at a certain point in stressed body. The magnitude of normal stresses in x and y directions are 100 MPa respectively. This radius of Mohr's stress circle representing this state stress is
- (a)
120
- (b)
80
- (c)
60
- (d)
40
A circular shaft of length L is held at two ends without rotation. A twisting moment T is applied at a distance L/3 from left as shown in the given figure. The twisting moment in the AB will be
- (a)
T
- (b)
T/3
- (c)
T/2
- (d)
2T/3
A cantilever beam is loaded as shown in the figure, the deflection at point C will be
- (a)
\(\frac { 7wL^{ 4 } }{ 2592EI } \)
- (b)
\(\frac { 7wL^{ 4 } }{ 1944EI } \)
- (c)
\(\frac { 7wL^{ 4 } }{ 1296EI } \)
- (d)
\(\frac { 7wL^{ 4 } }{ 848EI } \)
1654060945.png)
1654060942.png)
1653987551.png)
1653987086.png)
1582095229.jpg)
