(B) The formula for stress is given by $\text{Stress} = \frac{F}{A}$,where $F$ is the force (load) and $A$ is the cross-sectional area.Given radius $r

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(B) The formula for stress is given by $\text{Stress} = \frac{F}{A}$,where $F$ is the force (load) and $A$ is the cross-sectional area.Given radius $r = 1.5 \; cm = 0.015 \; m$.The cross-sectional area $A = \pi r^2 = \pi (0.015)^2 \; m^2$.Given maximum stress $\sigma_{max} = 10^8 \; N m^{-2}$.Maximum load $F_{max} = \sigma_{max} \times A$.$F_{max} = 10^8 \times \pi \times (0.015)^2$.$F_{max} = 10^8 \times 3.14159 \times 0.000225$.$F_{max} = 7.0685 \times 10^4 \; N \approx 7.065 \times 10^4 \; N$.Thus,the cable can support a maximum load of $7.065 \times 10^4 \; N$.

Class 11 Physics Mechanical Properties of Solids Basic of Elasticity, Stress and Strain relationship and Graphical analysis

Easy

$A$ steel cable with a radius of $1.5 \; cm$ supports a chairlift at a ski area. If the maximum stress is not to exceed $10^{8} \; N m^{-2}$,what is the maximum load the cable can support?

A
$6.035 \times 10^{6} \; N$
B
$7.065 \times 10^{4} \; N$
C
$2.56 \times 10^{3} \; N$
D
$6.425 \times 10^{5} \; N$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Mechanical Properties of Solids

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Basic of Elasticity, Stress and Strain relationship and Graphical analysis

If the side of a cube decreases by $1\%$,the volume strain is ........ $\%$.

Easy

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$A$ metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14\,mm$. The tensile stress developed in the wire under equilibrium state is $7 \times 10^5\,N m^{-2}$. The value of mass $m$ is $......kg$.
(Take,$g = 9.8\,m s^{-2}$ and $\pi = \frac{22}{7}$)

MediumJEE MAIN 2023

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Match the details of Column-$II$ with the given information in Column-$I$ appropriately.
Column-$I$ Column-$II$
$(a)$ Stress is proportional to strain. $(i)$ Elastic limit
$(b)$ When the load on the wire is removed, the body regains its original dimension. $(ii)$ Limit of proportionality
$(iii)$ Plastic deformation

Easy

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The load versus elongation graph for four wires of the same material is shown in the figure. The thinnest wire is represented by the line

MediumMHT CET 2011

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Match List-$I$ with List-$II$ :
List-$I$ List-$II$
$(A)$ $A$ force that restores an elastic body of unit area to its original state $(I)$ Bulk modulus
$(B)$ Two equal and opposite forces parallel to opposite faces $(II)$ Young's modulus
$(C)$ Forces perpendicular everywhere to the surface per unit area same everywhere $(III)$ Stress
$(D)$ Two equal and opposite force perpendicular to opposite faces $(IV)$ Shear modulus

Choose the correct answer from the options given below:

List-$I$	List-$II$
$(A)$ $A$ force that restores an elastic body of unit area to its original state	$(I)$ Bulk modulus
$(B)$ Two equal and opposite forces parallel to opposite faces	$(II)$ Young's modulus
$(C)$ Forces perpendicular everywhere to the surface per unit area same everywhere	$(III)$ Stress
$(D)$ Two equal and opposite force perpendicular to opposite faces	$(IV)$ Shear modulus

DifficultJEE MAIN 2024

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Column-$I$	Column-$II$
$(a)$ Stress is proportional to strain.	$(i)$ Elastic limit
$(b)$ When the load on the wire is removed, the body regains its original dimension.	$(ii)$ Limit of proportionality
	$(iii)$ Plastic deformation

$A$ steel cable with a radius of $1.5 \; cm$ supports a chairlift at a ski area. If the maximum stress is not to exceed $10^{8} \; N m^{-2}$,what is the maximum load the cable can support?

Similar Questions

If the side of a cube decreases by $1\%$,the volume strain is ........ $\%$.

$A$ metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14\,mm$. The tensile stress developed in the wire under equilibrium state is $7 \times 10^5\,N m^{-2}$. The value of mass $m$ is $......kg$.(Take,$g = 9.8\,m s^{-2}$ and $\pi = \frac{22}{7}$)

The load versus elongation graph for four wires of the same material is shown in the figure. The thinnest wire is represented by the line

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$A$ metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14\,mm$. The tensile stress developed in the wire under equilibrium state is $7 \times 10^5\,N m^{-2}$. The value of mass $m$ is $......kg$.
(Take,$g = 9.8\,m s^{-2}$ and $\pi = \frac{22}{7}$)