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JEE Mains | PYQ

If average depth of an ocean is \( 4000 \, \text{m} \) and the bulk modulus of water is \( 2 \times 10^{9} \, \text{N m}^{-2} \), then fractional compression \( \dfrac{\Delta V}{V} \) of water at the bottom of ocean is \( \alpha \times 10^{-2} \). The value of \( \alpha \) is ________.
(Given, \( g = 10 \, \text{ms}^{-2} \), \( \rho = 1000 \, \text{kgm}^{-3} \) )

Young's modules of material of a wire of length '\( L \)' and cross-sectional area \( A \) is \( Y \). If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be:

A block of ice at \( -10^\circ \text{C} \) is slowly heated and converted to steam at \( 100^\circ \text{C} \). Which of the following curves represent the phenomenon qualitatively:

Each of three blocks \( P \), \( Q \) and \( R \) shown in figure has a mass of \( 3 \, \text{kg} \). Each of the wires \( A \) and \( B \) has cross-sectional area \( 0.005 \, \text{cm}^2 \) and Young's modulus \( 2 \times 10^{11} \, \text{N} \, \text{m}^{-2} \). Neglecting friction, the longitudinal strain on wire \( B \) is _____ \( \times 10^{4} \). (Take \( g = 10 \, \text{m} / \text{s}^{2} \) )

An elastic spring under tension of \( 3\,\text{N} \) has a length \( a \). Its length is \( b \) under tension \( 2\,\text{N} \). For its length \( (3a - 2b) \), the value of tension will be _________ \( \text{N} \).

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

With rise in temperature, the Young’s modulus of elasticity:

A wire of length \( L \) and radius \( r \) is clamped at one end. If its other end is pulled by a force \( F \), its length increases by \( l \). If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by \( 0.02\% \) is \( \_\_\_ \, \text{m} \). (Take density of sea water \( = 10^{3} \, \text{kg m}^{-3} \). Bulk modulus of rubber \( = 9 \times 10^{8} \, \text{N m}^{-2} \), and \( g = 10 \, \text{m s}^{-2} \) )

Match List-I with List-II:

Choose the correct answer from the options given below:

On celcius scale the temperature of body increases by \( 40^\circ \text{C} \). The increase in temperature on Fahrenheit scale is:

A wire of cross sectional area \( A \), modulus of elasticity \( 2\times 10^{11}\,\text{N m}^{-2} \) and length \( 2\,\text{m} \) is stretched between two vertical rigid supports. When a mass of \( 2\,\text{kg} \) is suspended at the middle it sags lower from its original position making angle \( \theta=\dfrac{1}{100} \) radian on the points of support. The value of \( A \) is ______ \( \times 10^{-4} \) \( \text{m}^{2} \) (consider \( x\ll L \)). (given: \( g=10\,\text{m/s}^{2} \))

A spherical call of radius \(1 \times 10^{-4} \, \text{m}\) and density \(10^{5} \, \text{kg/m}^{3}\) falls freely under gravity through a distance \(h\) before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of \(h\) is approximately:
(The coefficient of viscosity of water is \(9.8 \times 10^{-6} \, \text{N s/m}^{2}\))

Two persons pull a wire towards themselves. Each person exerts a force of \( 200 \, \text{N} \) on the wire. Young's modulus of the material of wire is \( 1 \times 10^{11} \, \text{N m}^{-2} \). Original length of the wire is \( 2 \, \text{m} \) and the area of cross section is \( 2 \, \text{cm}^{2} \). The wire will extend in length by ________ \( \mu \text{m} \).

A straight magnetic strip has a magnetic moment of \( 44 \, \text{Am}^2 \). If the strip is bent in a semicircular shape, its magnetic moment will be ____ \( \text{Am}^2 \).
\( \left( \text{given } \pi = \frac{22}{7} \right) \)

Two metallic wires \( P \) and \( Q \) have same volume and are made up of same material. If their area of cross sections are in the ratio \( 4:1 \) and force \( F_{1} \) is applied to \( P \), an extension of \( \Delta l \) is produced. The force which is required to produce same extension in \( Q \) is \( F_{2} \). The value of \( \dfrac{F_{1}}{F_{2}} \) is __________.

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 most appropriate answer from the options given below:

One end of a metal wire is fixed to a ceiling and a load of \( 2 \, \text{kg} \) hands from the other end. A similar wire is attached to the bottom of the load and anther load of \( 1 \, \text{kg} \) hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________.
[Area of cross section of wire \( = 0.005 \, \text{cm}^2 \); \( Y = 2 \times 10^{11} \, \text{N m}^{-2} \) and \( g = 10 \, \text{m s}^{-2} \)]

Two conductors have the same resistance at \( 0^\circ \text{C} \) but their temperature coefficients of resistance are \( \alpha_{1} \) and \( \alpha_{2} \). The respective temperature coefficients for their series and parallel combinations are: