Mechanical Properties of Solids Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. For the same cross-sectional area and for a given  load, the ratio of
depressions for the beam of a square cross-section and circular cross-
section is
(a) 3 : p
(b) p : 3
(c) 1 : p
(d) p : 1
2. A metal rod of Young’s modulus 2 × 10
10
 N m
–2
 undergoes an elastic
strain of 0.06%. The energy per unit volume stored in J m
–3
 is
(a) 3600
(b) 7200
(c) 10800
(d) 14400
3. The length of an elastic string is a metre  when the longitudinal tension
is 4 N and b metre when the longitudinal tension is 5 N. The length of
the string in metre when the longitudinal tension is 9 N is
Page 2


PART-I (Single Correct MCQs)
1. For the same cross-sectional area and for a given  load, the ratio of
depressions for the beam of a square cross-section and circular cross-
section is
(a) 3 : p
(b) p : 3
(c) 1 : p
(d) p : 1
2. A metal rod of Young’s modulus 2 × 10
10
 N m
–2
 undergoes an elastic
strain of 0.06%. The energy per unit volume stored in J m
–3
 is
(a) 3600
(b) 7200
(c) 10800
(d) 14400
3. The length of an elastic string is a metre  when the longitudinal tension
is 4 N and b metre when the longitudinal tension is 5 N. The length of
the string in metre when the longitudinal tension is 9 N is
(a) a – b
(b) 5b – 4a
(c)
(d) 4a – 3b
4. A beam of metal supported at the two edges is loaded at the centre. The
depression at the centre is proportional to
(a) Y 
2
(b) Y
(c) 1/Y
(d) 1/Y 
2
5. A structural steel rod has a radius of 10 mm and length of  1.0 m. A 100
kN force stretches it along its length. Young’s modulus of structural
steel is 2 × 10
11
 Nm
–2
. The percentage strain is about
(a) 0.16%
(b) 0.32%
(c) 0.08%
(d) 0.24%
6. The upper end of a wire of diameter 12mm and length 1m is clamped
and its other end is twisted through an angle of 30°. The angle of shear
is
(a) 18°
(b) 0.18°
(c) 36°
(d) 0.36°
7. The graph given is a stress-strain curve for
(a) elastic objects
(b) plastics
(c) elastomers
(d) None of these
Page 3


PART-I (Single Correct MCQs)
1. For the same cross-sectional area and for a given  load, the ratio of
depressions for the beam of a square cross-section and circular cross-
section is
(a) 3 : p
(b) p : 3
(c) 1 : p
(d) p : 1
2. A metal rod of Young’s modulus 2 × 10
10
 N m
–2
 undergoes an elastic
strain of 0.06%. The energy per unit volume stored in J m
–3
 is
(a) 3600
(b) 7200
(c) 10800
(d) 14400
3. The length of an elastic string is a metre  when the longitudinal tension
is 4 N and b metre when the longitudinal tension is 5 N. The length of
the string in metre when the longitudinal tension is 9 N is
(a) a – b
(b) 5b – 4a
(c)
(d) 4a – 3b
4. A beam of metal supported at the two edges is loaded at the centre. The
depression at the centre is proportional to
(a) Y 
2
(b) Y
(c) 1/Y
(d) 1/Y 
2
5. A structural steel rod has a radius of 10 mm and length of  1.0 m. A 100
kN force stretches it along its length. Young’s modulus of structural
steel is 2 × 10
11
 Nm
–2
. The percentage strain is about
(a) 0.16%
(b) 0.32%
(c) 0.08%
(d) 0.24%
6. The upper end of a wire of diameter 12mm and length 1m is clamped
and its other end is twisted through an angle of 30°. The angle of shear
is
(a) 18°
(b) 0.18°
(c) 36°
(d) 0.36°
7. The graph given is a stress-strain curve for
(a) elastic objects
(b) plastics
(c) elastomers
(d) None of these
8. A circular tube of mean radius 8 cm and thickness 0.04 cm is melted up
and recast into a solid rod of the same length. The ratio of the torsional
rigidities of the circular tube and the solid rod is
(a)
(b)
(c)
(d)
9. If the ratio of lengths, radii and Young’s moduli of steel
and brass wires in the figure are a, b and c respectively,
then the corresponding ratio of increase in their lengths is
:
(a)
(b)
(c)
(d)
10. Copper of fixed volume ‘V; is drawn into wire of length ‘l’. When this
wire is subjected to a constant force ‘F’, the extension produced in the
wire is ‘?l’. Which of the following graphs is a straight line?
(a) ?l versus 
(b) ?l versus l
2
Page 4


PART-I (Single Correct MCQs)
1. For the same cross-sectional area and for a given  load, the ratio of
depressions for the beam of a square cross-section and circular cross-
section is
(a) 3 : p
(b) p : 3
(c) 1 : p
(d) p : 1
2. A metal rod of Young’s modulus 2 × 10
10
 N m
–2
 undergoes an elastic
strain of 0.06%. The energy per unit volume stored in J m
–3
 is
(a) 3600
(b) 7200
(c) 10800
(d) 14400
3. The length of an elastic string is a metre  when the longitudinal tension
is 4 N and b metre when the longitudinal tension is 5 N. The length of
the string in metre when the longitudinal tension is 9 N is
(a) a – b
(b) 5b – 4a
(c)
(d) 4a – 3b
4. A beam of metal supported at the two edges is loaded at the centre. The
depression at the centre is proportional to
(a) Y 
2
(b) Y
(c) 1/Y
(d) 1/Y 
2
5. A structural steel rod has a radius of 10 mm and length of  1.0 m. A 100
kN force stretches it along its length. Young’s modulus of structural
steel is 2 × 10
11
 Nm
–2
. The percentage strain is about
(a) 0.16%
(b) 0.32%
(c) 0.08%
(d) 0.24%
6. The upper end of a wire of diameter 12mm and length 1m is clamped
and its other end is twisted through an angle of 30°. The angle of shear
is
(a) 18°
(b) 0.18°
(c) 36°
(d) 0.36°
7. The graph given is a stress-strain curve for
(a) elastic objects
(b) plastics
(c) elastomers
(d) None of these
8. A circular tube of mean radius 8 cm and thickness 0.04 cm is melted up
and recast into a solid rod of the same length. The ratio of the torsional
rigidities of the circular tube and the solid rod is
(a)
(b)
(c)
(d)
9. If the ratio of lengths, radii and Young’s moduli of steel
and brass wires in the figure are a, b and c respectively,
then the corresponding ratio of increase in their lengths is
:
(a)
(b)
(c)
(d)
10. Copper of fixed volume ‘V; is drawn into wire of length ‘l’. When this
wire is subjected to a constant force ‘F’, the extension produced in the
wire is ‘?l’. Which of the following graphs is a straight line?
(a) ?l versus 
(b) ?l versus l
2
(c) ?l versus 
(d) ?l versus l
11. An elastic string of unstretched length L and force constant k is
stretched by a small length x. It is further stretched by another small
length y. The work done in the second stretching is :
(a)
(b)
(c)
(d)
12. In materials like aluminium and copper, the correct order of magnitude
of various elastic modului is:
(a) Young’s modulus < shear modulus < bulk modulus.
(b) Bulk modulus < shear modulus < Young’s modulus
(c) Shear modulus < Young’s modulus < bulk modulus.
(d) Bulk modulus < Young’s modulus < shear modulus.
13. A cube at temperature 0ºC is compressed equally from all sides by an
external pressure P. By what amount should its temperature be raised to
bring it back to the size it had before the external pressure was applied.
The bulk modulus of the material of the cube is B and the coefficient of
linear expansion is a.
(a) P/B a
(b) P/3 B a
(c) 3 p a/B
(d) 3 B/P
14. Stress Vs strain for the elastic tissue of the aorta, the large tube (vessel)
carrying blood from the heart, will be : [stress is proportional to square
of the strain for the elastic tissue of the aorta]
Page 5


PART-I (Single Correct MCQs)
1. For the same cross-sectional area and for a given  load, the ratio of
depressions for the beam of a square cross-section and circular cross-
section is
(a) 3 : p
(b) p : 3
(c) 1 : p
(d) p : 1
2. A metal rod of Young’s modulus 2 × 10
10
 N m
–2
 undergoes an elastic
strain of 0.06%. The energy per unit volume stored in J m
–3
 is
(a) 3600
(b) 7200
(c) 10800
(d) 14400
3. The length of an elastic string is a metre  when the longitudinal tension
is 4 N and b metre when the longitudinal tension is 5 N. The length of
the string in metre when the longitudinal tension is 9 N is
(a) a – b
(b) 5b – 4a
(c)
(d) 4a – 3b
4. A beam of metal supported at the two edges is loaded at the centre. The
depression at the centre is proportional to
(a) Y 
2
(b) Y
(c) 1/Y
(d) 1/Y 
2
5. A structural steel rod has a radius of 10 mm and length of  1.0 m. A 100
kN force stretches it along its length. Young’s modulus of structural
steel is 2 × 10
11
 Nm
–2
. The percentage strain is about
(a) 0.16%
(b) 0.32%
(c) 0.08%
(d) 0.24%
6. The upper end of a wire of diameter 12mm and length 1m is clamped
and its other end is twisted through an angle of 30°. The angle of shear
is
(a) 18°
(b) 0.18°
(c) 36°
(d) 0.36°
7. The graph given is a stress-strain curve for
(a) elastic objects
(b) plastics
(c) elastomers
(d) None of these
8. A circular tube of mean radius 8 cm and thickness 0.04 cm is melted up
and recast into a solid rod of the same length. The ratio of the torsional
rigidities of the circular tube and the solid rod is
(a)
(b)
(c)
(d)
9. If the ratio of lengths, radii and Young’s moduli of steel
and brass wires in the figure are a, b and c respectively,
then the corresponding ratio of increase in their lengths is
:
(a)
(b)
(c)
(d)
10. Copper of fixed volume ‘V; is drawn into wire of length ‘l’. When this
wire is subjected to a constant force ‘F’, the extension produced in the
wire is ‘?l’. Which of the following graphs is a straight line?
(a) ?l versus 
(b) ?l versus l
2
(c) ?l versus 
(d) ?l versus l
11. An elastic string of unstretched length L and force constant k is
stretched by a small length x. It is further stretched by another small
length y. The work done in the second stretching is :
(a)
(b)
(c)
(d)
12. In materials like aluminium and copper, the correct order of magnitude
of various elastic modului is:
(a) Young’s modulus < shear modulus < bulk modulus.
(b) Bulk modulus < shear modulus < Young’s modulus
(c) Shear modulus < Young’s modulus < bulk modulus.
(d) Bulk modulus < Young’s modulus < shear modulus.
13. A cube at temperature 0ºC is compressed equally from all sides by an
external pressure P. By what amount should its temperature be raised to
bring it back to the size it had before the external pressure was applied.
The bulk modulus of the material of the cube is B and the coefficient of
linear expansion is a.
(a) P/B a
(b) P/3 B a
(c) 3 p a/B
(d) 3 B/P
14. Stress Vs strain for the elastic tissue of the aorta, the large tube (vessel)
carrying blood from the heart, will be : [stress is proportional to square
of the strain for the elastic tissue of the aorta]
(a)
(b)
(c)
(d)
15. A metal wire of length L
1
 and area of cross-section A is attached to a
rigid support. Another metal wire of length L
2
and of the same cross-sectional area is attached to the free end of the first
wire. A body of mass M is then suspended from the free end of the
second wire. If Y
1
 and Y
2
 are the Young’s moduli of the wires
respectively, the effective force constant of the system of two wires is
(a)
(b)
(c)
(d)
16. For a constant hydraulic stress on an object, the fractional change in the