A bar of cross-sectional area A is subjected | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the cross-sectional area of the bar be $A$. The force $F$ acts perpendicular to the cross-section of area $A$.Consider a plane $BB'$ inclined

Vedclass · Accepted Answer

$tan\, 	heta$

Vedclass · Answer

(A) Let the cross-sectional area of the bar be $A$. The force $F$ acts perpendicular to the cross-section of area $A$.Consider a plane $BB'$ inclined at an angle $	heta$ with the length of the bar. The normal to this plane makes an angle $	heta$ with the direction of the force $F$.The area of the inclined plane $BB'$ is $A' = A / \sin 	heta$.The force $F$ can be resolved into two components relative to the plane $BB'$:$1$. Normal force component: $F_N = F \sin 	heta$ (acting perpendicular to the plane $BB'$).$2$. Tangential (shearing) force component: $F_S = F \cos 	heta$ (acting along the plane $BB'$).The tensile stress (normal stress) on plane $BB'$ is $\sigma = F_N / A' = (F \sin 	heta) / (A / \sin 	heta) = (F / A) \sin^2 	heta$.The shearing stress on plane $BB'$ is $	au = F_S / A' = (F \cos 	heta) / (A / \sin 	heta) = (F / A) \sin 	heta \cos 	heta$.The ratio of tensile stress to shearing stress is:$\frac{\sigma}{	au} = \frac{(F/A) \sin^2 	heta}{(F/A) \sin 	heta \cos 	heta} = \frac{\sin 	heta}{\cos 	heta} = 	an 	heta$.

Column-$I$	Column-$II$
$(a)$ $\text{Stress} \propto \text{Strain}$	$(i)$ $M^1 L^{-1} T^{-2}$
$(b)$ $\text{Dimensional formula for compressibility}$	$(ii)$ $M^{-1} L^1 T^2$
	$(iii)$ $\text{Poisson's ratio}$
	$(iv)$ $\text{Hooke's law}$

$A$ bar of cross-sectional area $A$ is subjected to two equal and opposite tensile forces at its ends as shown in the figure. Consider a plane $BB'$ making an angle $\theta$ with the length. The ratio of tensile stress to the shearing stress on the plane $BB'$ is

Similar Questions

Is it possible to double the length of a metallic wire by applying force over it?

$A$ wire of length $40 \text{ cm}$ is stretched by $0.1 \text{ cm}$. The strain on the wire is

Check if the following statements are True or False:
$(a)$ Shear modulus of liquid is infinite.
$(b)$ For a given load (external force),steel is more deformed than rubber.
$(c)$ When a solid body is beaten,rolled,heated,or cooled,its elastic properties are affected.

The breaking stress for a wire of radius $r$ of a given material is $F \ Nm^{-2}$. The breaking stress for a wire of the same material of radius $2r$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module