Strength of Material Sheet 25

1) Question.

Two identical bars, one simply supported and other fixed at ends, are acted upon by equal loads applied at the midpoints. The ratio of strain energy stored in the simply supported beam and the fixed ended beam is
Answer.
- 1
  
  1
- 2
  
  2
- 3
  
  3
- 4
  
  4
Answer: 4

Explanation:
2) Question.

Two circular bars A and B of same material and same length are of diameters $D_{A}$ and $D_{B}$ respectively. The bars are subjected to the same torque T. The ratio of strain energies stored in the bars A and B is proportional to
Answer.
- 1
  
  $\frac{D_{A}}{D_{B}}$
- 2
  
  $\frac{D_{B}}{D_{A}}$
- 3
  
  ${(\frac{D_{A}}{D_{B}})}^{2}$
- 4
  
  ${(\frac{D_{B}}{D_{A}})}^{4}$
Answer: 4

Explanation:
3) Question.

A steel rod of cross sectional area equal to $1000 m m^{2}$ is 5 m long. If a pull of 100 kN is suddenly applied to it, then the maximum stess intensity will be
Answer.
- 1
  
  $50 N / m m^{2}$
- 2
  
  $100 N / m m^{2}$
- 3
  
  $200 N / m m^{2}$
- 4
  
  $400 N / m m^{2}$
Answer: 3

Explanation:
4) Question.

A rectangular block of size 200 mm x 100 mm x 50 mm is subjected to a shear stress of 100 $N / m m^{2}$ . If modulus of rigidity of material is $1 x 10^{5} N / m m^{2}$ , strain energy stored will be
Answer.
- 1
  
  10 N. m
- 2
  
  25 N.m
- 3
  
  50 N.m
- 4
  
  100 N.m
Answer: 3

Explanation:
5) Question.

The radius of gyration of a circle of radius R is euqal to
Answer.
- 1
  
  R/4
- 2
  
  R/2
- 3
  
  R/√2
- 4
  
  R
Answer: 2

Explanation:
6) Question.

If a shaft of diameter d is subjected to a torque T and a bending moment M, the maximum shear stress is
Answer.
- 1
  
  $\frac{16 \sqrt{M^{2} - T^{2}}}{{πd}^{3}}$
- 2
  
  $\frac{16 \sqrt{M^{2} + T^{2}}}{{πd}^{3}}$
- 3
  
  $\frac{16}{{πd}^{3}} (M - \sqrt{M^{2} - T^{2}})$
- 4
  
  $\frac{16}{{πd}^{3}} (M + \sqrt{M^{2} - T^{2}})$
Answer: 2

Explanation:
7) Question.

If a circular shaft is subjected to a torque T and bending moment M, the ratio of maximum bending stress and maximum shear stress is
Answer.
- 1
  
  $\frac{2 M}{T}$
- 2
  
  $\frac{M}{2 T}$
- 3
  
  $\frac{M}{T}$
- 4
  
  $\frac{2 T}{M}$
Answer: 1

Explanation:
8) Question.

If the internal radius of a hollow shaft is n times the external radius, then ratio of torques carried by the hollow shaft and solid shaft of same cross-section area and subjected to the same maximum shearing stress is
Answer.
- 1
  
  $1 - n^{4}$
- 2
  
  $\frac{1 + n^{2}}{1 - n^{2}}$
- 3
  
  $\frac{\sqrt{1 + n^{2}}}{1 - n^{2}}$
- 4
  
  $\frac{1 + n^{2}}{\sqrt{1 - n^{2}}}$
Answer: 4

Explanation:
9) Question.

The ratio of strain energy stored by a hollow shaft of external diameter D and internal diameter d and strain energy stored by a solid shaft of diameter D is
Answer.
- 1
  
  $\frac{D^{2} + d^{2}}{D^{2}}$
- 2
  
  $\frac{D^{2} - d^{2}}{D^{2}}$
- 3
  
  $\frac{D^{4} - d^{4}}{D^{4}}$
- 4
  
  $\frac{D^{4} + d^{4}}{D^{4}}$
Answer: 1

Explanation:
10) Question.

A solid circular shaft of 6m length is built in at its ends and subjected to an extern ally applied torque 60 kN-m at a distance of 2 m from left end. The reactive torques at the left end and the right end are respectively
Answer.
- 1
  
  20 kN.m and 40 kN.m
- 2
  
  40 kN.m and 20 kN.m
- 3
  
  15 kN.m and 45 kN.m
- 4
  
  30 kN.m and 30 kN.m
Answer: 2

Explanation:
11) Question.

In a rectangular shaft subjected to torsion, the maximum shear stress occurs at
Answer.
- 1
  
  centre
- 2
  
  corners
- 3
  
  middle of smaller side
- 4
  
  middle of longer side
Answer: 4

Explanation:
12) Question.

If a shaft of diameter d is subjected to a torque, T, the maximum shear stress is
Answer.
- 1
  
  $\frac{32 T}{{πd}^{3}}$
- 2
  
  $\frac{16 T}{{πd}^{2}}$
- 3
  
  $\frac{16 T}{{πd}^{3}}$
- 4
  
  $\frac{64 T}{{πd}^{4}}$
Answer: 3

Explanation:
13) Question.

Consider a close coiled helical spring of radius $R,$ subjected to a load $P .$ The spring consists of $n$ turns of wire with wire radius $r .$ The stiffness of the spring is
Answer.
- 1
  
  $\frac{P R^{3}}{G I_{z}}$
- 2
  
  $\frac{G r^{4}}{4 n R^{3}}$
- 3
  
  $\frac{G I_{z} n r^{4}}{2 π R^{3}}$
- 4
  
  $\frac{P R^{4} 2 π n}{G I_{z}}$
Answer: 2

Explanation:
14) Question.

A cantilever beam $' A'$ with rectangular cross section is subjected to a concentrated load at its free end. If width and depth

of another cantilever beam $' B'$ are twice those of beam $A,$ then the deflection at free end of the beam $' B'$ as compared to

that of $' A'$ will be
Answer.
- 1
  
  $6.25 %$
- 2
  
  $14 %$
- 3
  
  $23.6 %$
- 4
  
  $28 %$
Answer: 1

Explanation:
15) Question.

A beam has a solid circular cross section having diameter $d .$ If a section of the beam is subjected to a shear force, $F,$ the maximum shear stress in the cross section is given by
Answer.
- 1
  
  $\frac{4}{3} \frac{F}{π d^{2}}$
- 2
  
  $\frac{16}{3} \frac{F}{π d^{2}}$
- 3
  
  $\frac{8}{3} \frac{F}{π d^{2}}$
- 4
  
  $\frac{3}{16} \frac{F}{π d^{2}}$
Answer: 2

Explanation:
16) Question.

A simply supported beam of uniform cross section is subjected to a maximum bending moment of $2.25$ $t . m .$ If it has

rectangular cross section with width $15 c m$ and depth $30 c m$ , then the maximum bending stress induced in the beam will be
Answer.
- 1
  
  $50 k g / c m^{2}$
- 2
  
  $100 k g / c m^{2}$
- 3
  
  $150 k g / c m^{2}$
- 4
  
  $225 k g / c m^{2}$
Answer: 2

Explanation:
17) Question.
Consider the following statements regarding a simply supported beam subjected to a uniformly distributed load over the entire span:
1. The bending moment is maximum at the central position.
2. The shear force is zero at the central position.
  1. The slope is maximum at the middle position.
Answer.
- 1
  
  $1, 2$ and $3$ are correct
- 2
  
  $1$ and $2$ are correct
- 3
  
  $2$ and $3$ are correct
- 4
  
  $1$ and $3$ are correct
Answer: 2

Explanation:
18) Question.

Sets of principal stresses acting at any point in a stressed body are given below:

1. $\{σ, 0\}$

2. $\{σ, σ\}$

3. $\{σ, - σ\}$

4. $\{σ, \frac{σ}{2}\}$
Answer.
- 1
  $1, 4, 3, 2$
- 2
  
  $2, 1, 4, 3$
- 3
  
  $1, 3, 4, 2$
- 4
  
  $2, 4, 1, 3$
Answer: 4

Explanation:
19) Question.

The material of a rubber ballon has Poission's ratio of $0.5 .$ If uniform pressure is applied to blow the ballon, the volumetric strain of the material will be
Answer.
- 1
  
  $0.50$
- 2
  
  $0.25$
- 3
  
  $0.20$
- 4
  
  Zero
Answer: 4

Explanation:
20) Question.

A composite section made of two materials has moduli of elasticity in the ratio $1 : 2$ and lengths in the ratio $2 : 1 .$ The ratio of corresponding stresses under a direct load is
Answer.
- 1
  
  $2 : 1$
- 2
  
  $1 : 2$
- 3
  
  $4 : 1$
- 4
  
  $1 : 4$
Answer: 3

Explanation:

Question Pallet

Time Left -