Q 1 :

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

 

Assertion (A): The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is elasticity.

 

Reason (R): The restoring force depends upon the bonded inter atomic and inter molecular force of solid.

 

In the light of the above statements, choose the correct answer from the given below:                                          [2024]

• (A) is false but (R) is true

   

• (A) is true but (R) is false

   

• Both (A) and (R) are true and (R) is the correct explanation of (A)

   

• Both (A) and (R) are true but (R) is not the correct explanation of (A)

   

Q 2 :

The density and breaking stress of a wire are $6\times {10}^4$$\mathrm{kg}/{\mathrm{m}}^3$ and $1.2\times {10}^8$$\mathrm{N}/{\mathrm{m}}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}rd$ of the value on the surface of Earth. The maximum length of the wire with breaking is _____ m (take, g = 10 $\mathrm{m}/{\mathrm{s}}^2$).            [2024]

Q 3 :

A $100\text{\hspace{0.05em}m}$ long wire having cross-sectional area $6.25\times {10}^{-4}{\text{\hspace{0.05em}m}}^2$ and Young's modulus is ${10}^{10}{\text{\hspace{0.05em}Nm}}^{-2}$ is subjected to a load of 250 N. Then the elongation in the wire will be:     [2023]

• $6.25\times {10}^{-3}\text{\hspace{0.05em}m}$

   

• $4\times {10}^{-3}\text{\hspace{0.05em}m}$

   

• $4\times {10}^{-4}\text{\hspace{0.05em}m}$

   

• $6.25\times {10}^{-6}\text{\hspace{0.05em}m}$

   

Q 4 :

A force is applied to a steel wire ‘A’, rigidly clamped at one end. As a result, elongation in the wire is 0.2 mm. If the same force is applied to another steel wire ‘B’ of double the length and a diameter 2.4 times that of the wire ‘A’, the elongation in the wire ‘B’ will be (wires having uniform circular cross sections).         [2023]

• $6.06\times {10}^{-2}\text{\hspace{0.05em}mm}$

   

• $2.77\times {10}^{-2}\text{\hspace{0.05em}mm}$

   

• $3.0\times {10}^{-2}\text{\hspace{0.05em}mm}$

   

• $6.9\times {10}^{-2}\text{\hspace{0.05em}mm}$

   

Q 5 :

A wire of length $\text{'}L\text{'}$ and radius $\text{'}\mathrm{r}\text{'}$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by $\text{'}l\text{'}$.

Another wire of the same material of length $\text{'}2L\text{'}$ and radius $\text{'}2r\text{'}$ is pulled by a force $\text{'}2f\text{'}$. Then the increase in its length will be:            [2023]

• $2l$

   

• $l$

   

• $4l$

   

• $\frac{l}{2}$

   

Q 6 :

A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is $2.0\times {10}^{11}{\text{N/m}}^2$. The longitudinal strain produced in the wire is __________ $\times {10}^{-5}$.             [2023]

Q 7 :

A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is $7\times {10}^5{\text{Nm}}^{-2}$. The value of mass $m$ is ________ kg. (Take, $g=9.8{\text{ms}}^{-2}$ and $\pi =\frac{22}{7}$)                [2023]

Q 8 :

A steel rod of length 1 m and cross-sectional area ${10}^{-4}{\text{\hspace{0.05em}m}}^2$ is heated from $0°\text{C}$ to $200°\text{C}$ without being allowed to extend or bend. The compressive tension produced in the rod is _______ $\times {10}^4\text{\hspace{0.05em}N}$. (Given Young's modulus of steel $=2\times {10}^{11}{\text{\hspace{0.05em}Nm}}^{-2}$, coefficient of linear expansion $={10}^{-5}{\text{\hspace{0.05em}K}}^{-1}$)             [2023]

Q 9 :

The length of a wire becomes $l_1$ and $l_2$ when 100 N and 120 N tensions are applied respectively. If $10 l_2=11 l_1$, the natural length of the wire will be $\frac{1}{x}{l}_1$. Here the value of $x$ is __________ .           [2023]