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1. A steel cable with a radius of \(1.5~\text{cm}\) supports a chairlift at a ski area. If the maximum stress is not to exceed \(10^{8}~\text{N/m}^2,\) what is the maximum load that the cable can support?
1. \(7.06\times 10^{4}~\text{N}\)
2. \(5.03\times 10^{4}~\text{N}\)
3. \(1.09\times 10^{4}~\text{N}\)
4. \(17\times 10^{4}~\text{N}\)

2.

Hooke's law is applicable for:

1.	elastic materials only	2.	plastic materials only
3.	elastomers only	4.	all of these

3.

The stress versus strain graph is shown for two wires. If \(Y_1\) and \(Y_2\) are Young modulus of wire \(A\) and \(B\) respectively, then the correct option is:

1.	\(Y_1>Y_2\)	2.	\(Y_2>Y_1\)
3.	\(Y_1=Y_2\)	4.	cannot say

4.

If the ratio of lengths, radii, and Young's modulus of steel and brass wires in the figure are \(a,\) \(b\) and \(c\) respectively, then the corresponding ratio of increase in their lengths will be:
                                 
1. \(\dfrac{2 a^{2} c}{b}\)
2. \(\dfrac{3 a}{2 b^{2} c}\)
3. \(\dfrac{2 a c}{b^{2}}\)
4. \(\dfrac{3 c}{2 a b^{2}}\)

5. A vessel of \(1\times 10^{-3}\) m³ volume contains oil. When a pressure of \(1.2 \times10^5\) N/m² is applied on it, then volume decreases by \(0.3 \times 10^{-6}\) m³. The bulk modulus of oil is:

1.	\(1 \times 10^6~\text{N/m}^2\)	2.	\(2 \times 10^7~\text{N/m}^2\)
3.	\(4 \times 10^8~\text{N/m}^2\)	4.	\(6 \times 10^{10}~\text{N/m}^2\)

6. The work done in stretching an elastic wire per unit volume is:

1.	stress\(\times\)strain
2.	\(\frac{1}{2}\) \(\times\) stress\(\times\)strain
3.	\(2\times\) stress\(\times\)strain
4.	stress/strain

7.

An elastic material of Young's modulus \(Y\) is subjected to a stress \(S\). The elastic energy stored per unit volume of the material is:
1. \(\frac{SY}{2}\)
2. \(\frac{S^2}{2Y}\)
3. \(\frac{S}{2Y}\)
4. \(\frac{2S}{Y}\)

8. When a block of mass \(M\) is suspended by a long wire of length \(L,\) the length of the wire becomes \((L+l).\) The elastic potential energy stored in the extended wire is:

1.	\(\dfrac{1}{2}MgL\)	2.	\(Mgl\)
3.	\(MgL\)	4.	\(\dfrac{1}{2}Mgl\)

9. Given below are two statements: 

Assertion (A):	Young's modulus for a perfectly plastic body is zero.
Reason (R):	For a perfectly plastic body, restoring force is zero.

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	Both (A) and (R) are False.

10.

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

1.	length = \(100~\text{cm},\) diameter = \(1~\text{mm}\)
2.	length = \(200~\text{cm},\) diameter = \(2~\text{mm}\)
3.	length = \(300~\text{cm},\) diameter = \(3~\text{mm}\)
4.	length = \(50~\text{cm},\) diameter = \(0.5~\text{mm}\)