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11
MCQ (Multiple Correct Answer)

A rod of length I and negligible mass is suspended at its two ends by two wires of steel (wire $A$ ) and aluminium (wire $B$ ) of equal lengths (figure). The cross-sectional areas of wires $A$ and $B$ are $1.0 \mathrm{~mm}^2$ and $2.0 \mathrm{~mm}^2$, respectively.

$\left(Y_{\mathrm{Al}}=70 \times 10^9 \mathrm{Nm}^{-2}\right.$ and $\left.Y_{\text {steel }}=200 \times 10^9 \mathrm{Nm}^{-2}\right)$

A
Mass $m$ should be suspended close to wire $A$ to have equal stresses in both the wires
B
Mass $m$ should be suspended close to $B$ to have equal stresses in both the wires
C
Mass $m$ should be suspended at the middle of the wires to have equal stresses in both the wires
D
Mass $m$ should be suspended close to wire $A$ to have equal strain in both wires
12
MCQ (Multiple Correct Answer)

For an ideal liquid,

A
the bulk modulus is infinite
B
the bulk modulus is zero
C
the shear modulus is infinite
D
the shear modulus is zero
13
MCQ (Multiple Correct Answer)

A copper and a steel wire of the same diameter are connected end to end. A deforming force $F$ is applied to this composite wire which causes a total elongation of 1 cm . The two wires will have

A
the same stress
B
different stress
C
the same strain
D
different strain
14
Subjective

The Young's modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?

Explanation

Young's modulus $(Y)=\frac{\text { Stress }}{\text { Longitudinal strain }}$

For same longitudinal strain, $\quad Y \propto$ stress

$$\therefore \quad \frac{Y_{\text {steel }}}{Y_{\text {rubber }}}=\frac{(\text { stress })_{\text {steel }}}{(\text { stress })_{\text {rubber }}} \quad \text{... (i)}$$

$$\begin{aligned} \text{But}\quad Y_{\text {steel }} & >Y_{\text {rubber }} \\ \frac{Y_{\text {steel }}}{Y_{\text {rubber }}} & >1 \end{aligned}$$

Therefore, from Eq. (i),

$$\begin{array}{ll} & \frac{(\text { stress })_{\text {steel }}}{(\text { stress })_{\text {rubber }}}>1 \\ \Rightarrow \quad & (\text { stress })_{\text {steel }}>(\text { stress })_{\text {rubber }} \end{array}$$

15
Subjective

Is stress a vector quantity?

Explanation

$$\text { Stress }=\frac{\text { Magnitude of internal reaction force }}{\text { Area of cross }- \text { section }}$$

Therefore, stress is a scalar quantity not a vector quantity.