DIRECTIONS: These are Assertion-Reason type questions. Each of these question contains two statements:Statement-1 (Assertion) and Statement-2 (Reason). Answer these questions from the following four options.

Statement 1:Strain causes the stress in an elastic body.

Statement 2:An elastic rubber is more plastic in nature.

(a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1
(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1
(c)Statement-1 is True, Statement- 2 is False
(d)Statement-1 is False, Statement -2 is True

Solution

(a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1

Statement 1:Young’s modulus for a perfectly plastic body is zero.

Statement 2:For a perfectly plastic body,restoring force iszero.

(a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1
(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1
(c)Statement-1 is True, Statement- 2 is False
(d)Statement-1 is False, Statement -2 is True

Solution

(d)Statement-1 is False, Statement -2 is True

Statement 1 : The stress-strain graphs are shown in the figure for two materials A and B are shown in figure. Young’s modulus of A is greater than that of B.

Statement 2 : The Young’s modules for small strain is,

\(\frac{stress}{strain}\)= slope of linear portion,of graph; and slope of A is more than slope that of B.

(a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1
(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1
(c)Statement-1 is True, Statement- 2 is False
(d)Statement-1 is False, Statement -2 is True

Solution

(d)Statement-1 is False, Statement -2 is True

Statement-1 Stress is the internal force per unit area of a body.

Statement-2 Rubber is less elastic than steel.

(a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1
(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1
(c)Statement-1 is True, Statement- 2 is False
(d)Statement-1 is False, Statement -2 is True

Solution

(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1

Stress is defined as internal force (restoring force) perunit area of a body. Also, rubber is less elastic than steel, because restoring force is less for rubber than steel.

Statement-1 Identical springs of steel and copper are equally stretched. More work will be done on the steel spring.

Statement-2 Steel is more elastic than copper.

(a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1
(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1
(c)Statement-1 is True, Statement- 2 is False
(d)Statement-1 is False, Statement -2 is True

Solution

(a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1

Work done =¹⁄₂ × Stress × Strain =¹⁄₂ × Y × (Strain)²

Since, elasticity of steel is more than copper, hence more work has to be done in order to stretch the steel.

A steel rod of radius R = 10mm and length L= 100 cm is stretched along its length by a force F = 6.28 ×10⁴ N. If the Young’s modulus of steel is Y = 2 × 10¹¹ N/m²,the percentage elongation in the length of the rod is :

0.100
0.314
2.015
1.549

Solution

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

Length = 100 cm, diameter = 1 mm
Length = 100 cm, diameter = 1 mm
Length = 100 cm, diameter = 1 mm
Length = 100 cm, diameter = 1 mm

Solution

When a 4 kg mass is hung vertically on a light spring that obeys Hooke’s law, the spring stretches by 2 cms. The work required to be done by an external agent in stretching this spring by 5 cms will be (g = 9.8 m/sec²)

4.900 joule
2.450 joule
0.495 joule
0.245 joule

Solution

A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

0.01
0.06
0.02
0.03

Solution

If the ratio of lengths, radii and Young’s modulus of steel and brass wires shown in the figure are a, b, and c, respectively. The ratio between the increase in lengths of brass and steel wires would be

\(\frac{b^{2}a}{2c}\)
\(\frac{bc}{2a^{2}}\)
\(\frac{ba^{2}}{2c}\)
\(\frac{a}{2b^{2}c}\)

Solution

UnAttempted

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Attempted

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Complete