Two rods of different materials but identical geometry have thermal coefficients of linear expansion as $\mathrm{\alpha }$ and 5$\mathrm{\alpha }$. The rods are fixed between two rigid and massive walls and are heated to the same temperature. If there is no bending of the rods and the thermal stresses developed in them are equal, then the ratio of their Young's moduli is:

(1) 1: 1

(2) 1: 25

(3) 1: 10

(4) 5: 1

A metal rod has a length of 100 cm and a cross-section area of 1 ${\mathrm{cm}}^2$. By raising its temperature from 0°C to 100°C so that it is not permitted to expand or bend, the tension developed in the rod is: ($\mathrm{Y} = {10}^{12} \mathrm{dyne}/{\mathrm{cm}}^2$ and $\mathrm{\alpha } = {10}^{-5}$/°C)

(1) ${10}^8$ dyne

(2) ${10}^9$ dyne

(3) ${10}^{10}$ dyne

(4) ${10}^{14}$ dyne

The metal rod (Y = 2 x ${10}^{12}$ dyne/sq. cm) of the coefficient of linear expansion 1.6 x ${10}^{-5}$ per °C has its temperature raised by 20°C. The linear compressive stress to prevent the expansion of the rod is:

(1) 2.4 x ${10}^8$ dyne/sq. cm

(2) 3.2 x ${10}^8$ dyne/sq. cm

(3) 6.4 x ${10}^8$ dyne/sq. cm

(4) 1.6 x ${10}^8$ dyne/sq. cm

An aluminum rod of length 2m held fixed in a horizontal position from its one end has the other end free. When the temperature of rod increases by 100°C, the thermal stress produced in the rod will be ($\mathrm{\alpha }$ = 1.6 x ${10}^{-6}$/°C)

(1) Zero

(2) 0.08

(3) 0.1

(4) 0.4

A rod of length 40 cm is stretched between two rigid supports at zero tension. If the temperature is increased by 10°C, the stress produced in it is:

(Young's modulus, Y = 1.2x${10}^{12} \mathrm{N}/{\mathrm{m}}^2$, coefficient of linear expansion of rod = 2 x ${10}^{-5}$/°C)

(1) 2.4 x ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

(2) 1.2 x ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

(3) 3.6 × ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

(4) 4.8 x ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

A faulty thermometer reads freezing point and boiling point of water as $10°C and 90°C$ respectively, the correct value of temperature as it reads $50°C$ is

(1)  $20°C$

(2) $30°C$

(3) $40°C$

(4) $50°C$

Given below are two statements: 
 

Given below are two statements: 
 

A metal rod is placed on a smooth horizontal surface at temperature \(25^\circ ~\text{C}.\) Now temperature of the surroundings is increased up to \(100^\circ ~\text{C}\)$$, then during heating of the rod,

The temperature on Celsius scale is $45°\mathrm{C}$, then corresponding temperature on the Fahrenheit scale is

1. $113°\mathrm{F}$ 

2. $77°\mathrm{F}$

3. $100°\mathrm{F}$

4. $131°\mathrm{F}$