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Two wires as shown in the figure below, made of steel and have breaking stress of \( 12 \times 10^{8} \, \text{N/m}^{2} \). Area of cross-section of upper wire is \( 0.008 \, \text{cm}^{2} \) and of lower wire is \( 0.004 \, \text{cm}^{2} \). The maximum mass that can be added to pan without breaking any wire is ______ kg.
\( \text{(take } g = 10 \, \text{m/s}^{2} \text{)} \)

Two wires A and B made of different materials of lengths \( 6.0 \, \text{cm} \) and \( 5.4 \, \text{cm} \), respectively and area of cross sections \( 3.0 \times 10^{-5} \, \text{m}^{2} \) and \( 4.5 \times 10^{-5} \, \text{m}^{2} \), respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is \( x : 3 \). The value of \( x \) is \( \underline{\phantom{0}} \).

The two wires \( A \) and \( B \) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \( A \) and wire \( B \) is \( 20/11 \). When the joined wire is kept under certain tension the elongations in the wires \( A \) and \( B \) are equal. If the length of wire \( A \) is \( 2.2 \, \text{m} \), then the length of wire \( B \) is ______ \( \text{m} \).

A copper wire of length \( 3 \, \text{m} \) is stretched by \( 3 \, \text{mm} \) by applying an external force. The volume of the wire is \( 600 \times 10^{-6} \, \text{m}^3 \). The elastic potential energy stored in the wire in stretched condition would be ____________ \( \text{J} \).
(Given Young modules of copper\( = 1.1 \times 10^{11}\,\mathrm{N/m^2}\)

A metal string \( A \) is suspended from a rigid support and its free end is attached to a block of mass \( M \). Second block having mass \( 2M \) is suspended at the bottom of the first block using a string \( B \). The area of cross sections of strings \( A \) and \( B \) are same. The ratio of lengths of strings of \( A \) to \( B \) is \( 2 \) and the ratio of their Young's moduli is \( 0.5 \). The ratio of elongations in \( A \) to \( B \) is ________.

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?

The Young's modulus of steel wire of radius \( r \) and length \( L \) is \( Y \). If the radius \( r \) and length \( L \) of the wire are doubled then the value of \( Y \).

The increase in the pressure required to decrease the volume \( (\Delta V) \) of water is \( 6.3 \times 10^7 \, \text{N}/\text{m}^2 \). The percentage decrease in the volume is ________. (Bulk modulus of water \( = 2.1 \times 10^9 \, \text{N}/\text{m}^2 \))

A gas based geyser heats water flowing at the rate of \( 5.0 \) litres per minute from \( 27^{\circ}\text{C} \) to \( 87^{\circ}\text{C} \). The rate of consumption of the gas is ____________ \( \text{g}/\text{s} \).
\( \text{(Take heat of combustion of gas } = 5.0 \times 10^{4} \, \text{J}/\text{g} \text{ ) specific heat capacity of water } = 4200 \, \text{J}/\text{kg}\cdot{}^{\circ}\text{C}. \)

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ dare maintained at $100^\circ\text{C}$ and $40^\circ\text{C}$ respectively. Given the thermal conductivity of rod $x$ is three times of that of rod $y$. the temperature at junction points $B$ and $E$ are (close to):

A uniform wire of length \( l \) of weight \( w \) is suspended from the roof with a weight of \( W \) at the other end. The stress in the wire at \( \frac{1}{3} \) distance from the top is \( \left( \frac{W}{A} + \frac{2w}{\gamma A} \right) \) where, \( A \) is the cross sectional area of the wire. The value of \( \gamma \) is _________.

If an air bubble of diameter \( 2 \, \text{mm} \) rises steadily through a liquid of density \( 2000 \, \text{kg}/\text{m}^{3} \) at a rate of \( 0.5 \, \text{cm}/\text{s} \), then the coefficient of viscosity of liquid is ________ Poise. (Take \( g = 10 \, \text{m}/\text{s}^{2} \))

The temperature of a metal strip having coefficient of linear expansion \( \alpha \) is increased from \( T_1 \) to \( T_2 \) resulting in increase of its length by \( \Delta L_1 \). The temperature is further increased from \( T_2 \) to \( T_3 \) such that the increase in its length is \( \Delta L_2 \).
Given \( T_3 + T_1 = 2T_2 \) and \( T_2 - T_1 = \Delta T \), the value of \( \Delta L_2 \) is ________.

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of \( 120 \, \text{cm} \) at \( 30^\circ\text{C} \). The coefficient of linear expansion of aluminium and steel are \( 24 \times 10^{-6} \, / \, ^\circ\text{C} \) and \( 1.2 \times 10^{-5} \, / \, ^\circ\text{C} \), respectively. The length of this composite rod when its temperature is raised to \( 100^\circ\text{C} \), is ________ \( \text{cm} \).

A string \( A \) of length \( 0.314 \, \text{m} \) and Young's modulus \( 2\times 10^{10}\, \text{N}/\text{m}^2 \) is connected to another string \( B \) of length and Young's modulus both twice of those of \( A \). This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass \( 0.8 \, \text{kg} \). The net change in length of the combination is ______ \( \text{mm} \).
(radius of both the strings is \( 0.2 \, \text{mm} \) and acceleration due to gravity \( =10\, \text{m}/\text{s}^2 \) (Mass of both strings is to be neglected as compared to the mass of load

A brass wire of length \( 2 \, \text{m} \) and radius \( 1 \, \text{mm} \) at \( 27^\circ \text{C} \) is held taut between two rigid supports. Initially it was cooled to a temperature of \( -43^\circ \text{C} \) creating a tension \( T \) in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to \( 1.4T \), is _____ \( ^\circ \text{C} \).

\( 10 \, \text{kg} \) of ice at \( -10^\circ \text{C} \) is added to \( 100 \, \text{kg} \) of water to lower its temperature from \( 25^\circ \text{C} \). Consider no heat exchange to surroundings. The decrement to the temperature of water is _________ \( ^\circ \text{C} \). (specific heat of ice \( = 2100 \, \text{J/kg}\!\cdot\!^\circ \text{C} \), specific heat of water \( = 4200 \, \text{J/kg}\!\cdot\!^\circ \text{C} \), latest heat of fusion of ice \( = 3.36 \times 10^{5} \, \text{J} / \text{kg} \) )

The heat extracted out of \( x \) gram of water initially at \( 50^\circ \text{C} \) to cool it down to \( 0^\circ \text{C} \) is sufficient to evaporate \( (1000 - x) \) gram of water also initially at \( 50^\circ \text{C} \). The value of \( x \) (closest integer) is ____________ .
(Take latent heat of water \( 2256 \, \text{kJ/kg} \cdot \text{K} \), specific heat capacity of water \( 4200 \, \text{J/kg} \cdot \text{K} \))

Which of the following best represents the temperature versus heat supplied graph for water, in the range of \( -20^\circ \text{C} \) to \( 120^\circ \text{C} \)?

The surface tension of a soap bubble is \( 0.03 \, \text{N}/\text{m} \). The work done in increasing the diameter of bubble from \( 2 \, \text{cm} \) to \( 6 \, \text{cm} \) is \( \alpha \pi \times 10^{-4} \, \text{J} \). The value of \( \alpha \) is _________. (Take \( \pi = 3.14 \))

A cube has side length \( 5 \, \text{cm} \) and modulus of rigidity \( 10^{5} \, \text{N}/\text{m}^{2} \). The displacement produced by a force of \( 10 \, \text{N} \) in the upper face of cube is ______ \( \text{mm} \).

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JEE Main 2026 5th April Morning Shift

A cube has side length \( 5 \, \text{cm} \) and modulus of rigidity \( 10^{5} \, \text{N}/\text{m}^{2} \). The displacement produced by a force of \( 10 \, \text{N} \) in the upper face of cube is ______ \( \text{mm} \).