Mechanical Properties of Solids - Stress and Strain
forces on solids
Questions
A cable that can support a load of 800 N is cut into two equal parts. The maximum load that can be supported by either part is
- 100 N
- 400 N
- 800 N
- 1600 N
A uniform steel bar of cross-sectional area A and length L. is suspended so that it hangs vertically. The stress at the middle point of the bar is ( $\rho $ is the density of steel)
- $\frac{L}{2A} \rho g$
- $\frac{L\rho g}{2} $
- $\frac{LA}{\rho g}$
- $L\rho g$
On suspending a weight $Mg$ the length $l$ of elastic wire and area of cross section $A$ its length becomes double the initial length. The instantaneous stress action on the wire is:
- $\dfrac{Mg}{A}$
- $\dfrac{Mg}{2A}$
- $\dfrac{2Mg}{A}$
- $\dfrac{4Mg}{A}$
The velocity of the transverse waves in a wire of density $8000kg/m^3$ is $300 m/s$. The tensile stress in the wire is then
- $7.2\times10^8 N/m^2$
- $6.8\times10^8 N/m^2$
- $5.2\times10^8 N/m^2$
- $8.4\times10^8 N/m^2$
An external force of $10\ N$ acts normally on a square area of each side $50\ cm$. The stress produced in equilibrium state is
- $10\ N/m^{2}$
- $20\ N/m^{2}$
- $40\ N/m^{2}$
- $50\ N/m^{2}$
The length of wire is increased by $0.06%$ by a load of $40N$ whose tensile modulus is $20\times10^{10}N/M^2$.The subjected stress is
- $12\times10^{10}N/m^2$
- $1.2\times10^{8}N/m^2$
- $120N/m^2$
- $1.25\times10^6N/m^2$
According to $C.E$ van der Waal, the interatomic potential varies with the average interatomic distance $(R)$ as
- $R^{-1}$
- $R^{-2}$
- $R^{-4}$
- $R^{-6}$
Overall changes in volume and radii of a uniform cylindrical steel wire are $0.2% $ and $0.002%$ respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is $\left( {Y = 2.0 \times {{10}^{11}}N{m^{ - 2}}} \right)$
- $3.2 \times {10^9}N{m^{ - 2}}$
- $3.2 \times {10^7}N{m^{ - 2}}$
- $3.6 \times {10^9}N{m^{ - 2}}$
- $3.6 \times {10^7}N{m^{ - 2}}$
A steel wire has an ultimate strength of above $2.0 \times 10 ^ { 7 } \mathrm { kg } - \mathrm { w } \mathrm { J } / \mathrm { m } ^ { 2 }$ . How large a load can a
0.7$\mathrm { cm }$ in diameter steel wire hold before breaking?
- $700 \mathrm { kg } - \mathrm { wt }$
- $770 \mathrm { kg } - \mathrm { wt }$
- $300 \mathrm { kg } - \mathrm { wt }$
- None
If equal and opposite forces applied to a body tend to elongate it, the stress so produced is called
- Tensile stress
- Compressive stress
- Tangential stress
- Working stress
A rubber cord 10 m is suspended vertically . How much does is stretch under its own weight (density of rubber is $1500kg{ m }^{ -3 },Y=5\times { 10 }^{ 8 }{ Nm }^{ -2 },g={ ms }^{ -2 }$)
- $15\times { 10 }^{ -4 }m\quad $
- $7.5\times { 10 }^{ -4 }m\quad $
- $12\times { 10 }^{ -4}m $
- $25\times { 10 }^{ -4 }m\quad $
A copper wire of $1mm$ diameter is stretched by applying a force on $10N$. Find the stress in the wire.
- $1.273\times 10^7N/m^2$
- $1.373\times 10^7N/m^2$
- $1.473\times 10^7N/m^2$
- $1.573\times 10^7N/m^2$
When the inter molecular distance increases due to tensile force, then
- There is no force between the molecules
- There is a repulsive force between the molecules
- There is an attractive force between the molecules
- There is zero resultant force between the molecules
A steel rod of length $5\ m$ is fixed rigidly between two supports, $\alpha$ of steel$=12\times 10^{-6}/^{o}\ C$, $Y=2\times10^{12}Nm^{-2}$. With the increase in its temperature by $40^{o}\ C$, the stress developed in the rod is
- $9.6\times10^{5}\ Nm^{-2}$
- $9.6\times10^{6}\ Nm^{-2}$
- $9.6\times10^{7}\ Nm^{-2}$
- $9.6\times10^{8}\ Nm^{-2}$
A bar of cross-section A is subjected to equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle $\theta$ with the axis of the bar.
For what value of $\theta$ is the tensile stress maximum?
- 0
- 1
- cant say
- 90
A composite rod is 1000 mm long, its two ends are 40 $mm^2$ and 30 $mm^2$ in area and length are 300 mm and 200 mm respectively. The middle portion of the rod is 20 $mm^2$ in area and 500 mm long. If the rod is subjected to an axial tensile load of 1000 N, find its total elongation (in mm). (E = 200 GPa).
- 0.165
- 0.111
- 0.196
- none of the above
A steel wire AB of length 100 cm is fixed rigidly at points A and B in an aluminium frame as shown in the figure If the temperature of the system increases through 100C, then the excess stress produced in the steel wire relative to the aluminium? ${ \alpha } _{ \mu }=22\times { 10 }^{ -6 }{ / }^{ 0 }Cand{ \alpha } _{ stret }=11\times { 10 }^{ -6 }{ / }^{ 0 }C$ young 's modulus of steel is $2\times { 10 }^{ 31 }{ Nm }^{ -2 }$
- $2.2\times { 10 }^{ 5 }$Pa
- $22\times { 10 }^{ 2 }$Pa
- $2.2\times { 10 }^{ 2 }$Pa
- $220\times { 10 }^{ 2 }$Pa
A metal wire of length L, area of cross-section A and Young modulus Y behaves as a spring of spring constant
- $K= \frac{YA}{L}$
- $K= \frac{2YA}{L}$
- $K= \frac{YA}{2L}$
- $K= \frac{YL}{A}$
A steel rod of length $1m$ and radius $10mm$ is stretched by a force $100kN$ along its length. The stress produced in the rod is then
$\left( { Y } _{ steel }=2\times { 10 }^{ 11 }N\quad { m }^{ -2 } \right) $
- $3.18\times { 10 }^{ 6 }N\quad { m }^{ -2 }$
- $3.18\times { 10 }^{ 7 }N\quad { m }^{ -2 }\quad $
- $3.18\times { 10 }^{ 8 }N\quad { m }^{ -2 }$
- $3.18\times { 10 }^{ 9 }N\quad { m }^{ -2 }\quad $
One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and
a weight $W _{1}$ is suspended from its lower end. If S is the are of cross-section of the wire, the stress in
the wire at a height (3 L /4) from its lower end is :
- $W _{1}/S$
- $[W _{1}+(W/4)]/S$
- $[W _{1}+(3W/4)]/S$
- $W _{1}+(W)/S$