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(A) Consider a bar of cross-sectional area $A$ subjected to a tensile force $F$. Let the cross-section $PQRS$ be inclined at an angle $	heta$ with th

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(A) Consider a bar of cross-sectional area $A$ subjected to a tensile force $F$. Let the cross-section $PQRS$ be inclined at an angle $	heta$ with the plane perpendicular to the force $F$. The area of the inclined cross-section $PQRS$ is $A' = \frac{A}{\cos 	heta}$. The component of force $F$ normal to the cross-section $PQRS$ is $F_n = F \cos 	heta$. The tensile stress $\sigma$ on the cross-section $PQRS$ is given by: $\sigma = \frac{F_n}{A'} = \frac{F \cos 	heta}{A / \cos 	heta} = \frac{F}{A} \cos^2 	heta$. For the tensile stress $\sigma$ to be maximum,$\cos^2 	heta$ must be maximum. The maximum value of $\cos^2 	heta$ is $1$,which occurs when $	heta = 0^o$.

Column-$I$	Column-$II$
$(A)$ Shear modulus	$(I)$ Resistance to change in volume
$(B)$ Shearing stress	$(II)$ Proportionality constant
$(C)$ Elastic fatigue	$(III)$ Tangential stress
$(D)$ Modulus of elasticity	$(IV)$ Temporary loss of elastic property
	$(V)$ Resistance to change against deformation force

List-$I$	List-$II$
$A$. Young's Modulus	$I$. $\frac{Ad}{\Delta L}$
$B$. Compressibility	$II$. $\frac{FL}{A\Delta L}$
$C$. Bulk Modulus	$III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$
$D$. Poisson's Ratio	$IV$. $-\frac{\Delta D/D}{\Delta L/L}$

For the tensile stress on the cross-section $PQRS$ to be maximum,$\theta =$ ......... $^o$

Similar Questions

$A$ metal wire is clamped between two vertical walls. At $20 ^o C$,the unstrained length of the wire is exactly equal to the separation between the walls. If the temperature of the wire is decreased,the graph between elastic energy density $(u)$ and temperature $(T)$ of the wire is:

Match List-$I$ with List-$II$:

List-$I$ List-$II$

$A$. Young's Modulus $I$. $\frac{Ad}{\Delta L}$

$B$. Compressibility $II$. $\frac{FL}{A\Delta L}$

$C$. Bulk Modulus $III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$

$D$. Poisson's Ratio $IV$. $-\frac{\Delta D/D}{\Delta L/L}$

Which of the following affects the elasticity of a substance?

If the length of a wire is reduced to half,then it can hold the ......... load.

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