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In Millikan’s oil drop experiment, what is viscous force acting on an uncharged drop of radius \( 2.0 \times 10^{-5} \, \text{m} \) and density \( 1.2 \times 10^{3} \, \text{kg m}^{-3} \)? Take viscosity of liquid \( = 1.8 \times 10^{-5} \, \text{N s m}^{-2} \). (Neglect buoyancy due to air).

A steel rod with \( y=2.0\times10^{11}\ \text{Nm}^{-2} \) and \( \alpha=10^{-5}\,^\circ\text{C}^{-1} \) of length \( 4\,\text{m} \) and area of cross-sectional \( 10\,\text{cm}^2 \) is heated from \( ^\circ\text{C} \) and \( 400^\circ\text{C} \) without being allowed to extend. The tension produced in the rod is \( x\times10^5\,\text{N} \) where the value of \( x \) is:

When a rubber ball is taken to a depth of ________ \( \text{m} \) in deep sea, its volume decreases by \( 0.5\% \).
(The bulk modulus of rubber \( = 9.8 \times 10^{8} \, \text{N m}^{-2} \) Density of sea water \( = 10^{3} \, \text{kg m}^{-3} \), \( g = 9.8 \, \text{m/ s}^{2} \) )

If the rms speed of oxygen molecules at \( 0^{\circ}\text{C} \) is \( 160 \, \text{m/s} \), find the rms speed of hydrogen molecules at \( 0^{\circ}\text{C} \).

The area of cross-section of a railway track is \( 0.01 \, \mathrm{m^{2}} \). The temperature variation is \( 10^{\circ}\mathrm{C} \). Coefficient of linear expansion of material of track is \( 10^{-5} \, / ^{\circ}\mathrm{C} \). The energy stored per meter in the track is ______ \( \mathrm{J/m} \). (Young’s modulus of material of track is \( 10^{11} \, \mathrm{N \, m^{-2}} \))

The balloon carries a total load of \( 185 \, \text{kg} \) at normal pressure and temperature of \( 27^\circ \text{C} \). What load will the balloon carry on rising to a height at which the barometric pressure is \( 45 \, \text{cm} \) of \( \text{Hg} \) and the temperature \( -7^\circ \text{C} \). Assuming the volume constant?

Two identical metal wires of thermal conductivities \( K_1 \) and \( K_2 \) respectively are connected in series. The effective thermal conductivity of the combination is;

Four identical hollow cylindrical columns of mild steel support a big structure of mass \( 50 \times 10^{3} \, \text{kg} \). The inner and outer radii of each column are \( 50 \, \text{cm} \) and \( 100 \, \text{cm} \) respectively. Assuming uniform load distribution, calculate the compression strain of each column, [use \( Y = 2.0 \times 10^{11} \, \text{Pa} \), \( g = 9.8 \, \text{m} / \text{s}^{2} \)]

A uniform metallic wire is elongated by \( 0.04 \, \text{m} \) when subjected to a linear force \( F \). The elongation, if its length and diameter is doubled and subjected to the same force will be ______ \( \text{cm} \).

A body takes \( 4 \) min. to cool from \( 61^{\circ} \text{C} \) and \( 59^{\circ} \text{C} \). If the temperature of the surroundings is \( 30^{\circ} \text{C} \), the time taken by the body to cool from \( 51^{\circ} \text{C} \) to \( 49^{\circ} \text{C} \) is:

Two blocks of masses \( 3 \, \text{kg} \) and \( 5 \, \text{kg} \) are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \( \dfrac{24}{\pi} \times 10^{2} \, \text{N m}^{-2} \). What is the minimum radius of the wire? \( \text{(Take } g = 10 \, \text{m s}^{-2}\text{)} \).

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is:

The height of Victoria falls is \( 63 \, \text{m} \). What is the difference in temperature of water at the top and at the bottom of fall?
[Given: \( 1 \, \text{cal} = 4.2 \, \text{J} \) and specific heat of water \( = 1 \, \text{cal} \, \text{g}^{-1} \, {}^\circ\text{C}^{-1} \)]

The value of tension in a long thin metal wire has been changed from \( T_1 \) to \( T_2 \). The lengths of the metal wire at two different values of tension \( T_1 \) and \( T_2 \) are \( l_1 \) and \( l_2 \) respectively. The actual length of the metal wire is:

The temperature of equal masses of three different liquids \( x \), \( y \) and \( z \) are \( 10^{\circ}\text{C} \), \( 20^{\circ}\text{C} \) and \( 30^{\circ}\text{C} \) respectively. The temperature of mixture when \( x \) is mixed with \( y \) is \( 16^{\circ}\text{C} \) and that when \( y \) is mixed with \( z \) is \( 26^{\circ}\text{C} \). The temperature of mixture when \( x \) and \( z \) are mixed will be:

In order to determine the Young’s Modulus of a wire of radius \( 0.2 \, \text{cm} \) (measured using a scale of least count = \( 0.001 \, \text{cm} \)) and length \( 1 \, \text{m} \) (measured using a scale of least count = \( 1 \, \text{mm} \)), a weight of mass \( 1 \, \text{kg} \) (measured using a scale of least count = \( 1 \, \text{g} \)) was hanged to get the elongation of \( 0.5 \, \text{cm} \) (measured using a scale of least count \( 0.001 \, \text{cm} \)). What will be the fractional error in the value of Young’s Modulus determined by this experiment ?

Wires \( W_{1} \) and \( W_{2} \) are made of same material having the breaking stress of \( 1.25 \times 10^{9} \, \text{N} / \text{m}^{2} \). \( W_{1} \) and \( W_{2} \) have cross-sectional area of \( 8 \times 10^{-7} \, \text{m}^{2} \) and \( 4 \times 10^{-7} \, \text{m}^{2} \), respectively. Masses of \( 20 \, \text{kg} \) and \( 10 \, \text{kg} \) hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _______ \( \text{kg} \).
(Use: \( g = 10 \, \text{m/s}^{2} \))

Two thin metallic spherical shells of radii \(\ r_1 \) and \(\ r_2 \) \(\ (r_1 < r_2) \) are placed with their centres coinciding. A material of thermal conductivity \(\ K \) is filled in the space between the shells. The inner shell is maintained at temperature \(\ \theta_1 \) and the outer shell at temperature \(\ \theta_2 \, (\theta_1 < \theta_2) \). The rate at which heat flows radially through the material is:

Two spherical soap bubbles of radii \( r_1 \) and \( r_2 \) in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

The length of a metal wire is \( l_{1} \) when the tension in it is \( T_{1} \) and is \( l_{2} \) when the tension is \( T_{2} \). The natural length of the wire is:

A stone of mass \( 20 \, \text{g} \) is projected from a rubber catapult of length \( 0.1 \, \text{m} \) and area of cross section \( 10^{-6} \, \text{m}^{2} \) stretched by an amount \( 0.04 \, \text{m} \). Take velocity of the projected stone is ______ m/s.
(Young’s modulus of rubber \( = 0.5 \times 10^{9} \, \text{N} / \text{m}^{2} \))

Two separate wires A and B are stretched by \( 2 \, \text{mm} \) and \( 4 \, \text{mm} \) respectively, when they are subjected to a force of \( 2 \, \text{N}\). Assume that both the wires are made up of same material and the radius of wire B is \( 4 \) times that of the radius of wire A.
The length of the wires A and B are in the ratio of \( a : b \). Then \( \frac{a}{b} \) can be expressed as \( \frac{1}{x} \) where \( x \) is __________ .

Two wires of same length and radius are joined end to end and loaded. The young’s modulii of the materials of the two wires are \( Y_1 \) and \( Y_2 \). The combination behaves as a single wire then its Young’s modulus is:

An ideal gas is expanding such that \( PT^{3} = \text{constant} \). The coefficient of volume expansion of the gas is:

The water is filled upto height of \( 12 \, \text{m} \) in a tank having vertical sidewalls. A hole is made in one of the walls at a depth ‘\( h \)’ below the water level. The value of ‘\( h \)’ for which the emerging stream of water strikes the ground at the maximum range is _______ \( \text{m} \).

A rod \( CD \) of thermal resistance \( 10.0\,\mathrm{kW^{-1}} \) is joined at the middle of an identical rod \( AB \) as shown in figure. The ends \( A \), \( B \) and \( D \) are maintained at \( 200^\circ\mathrm{C} \), \( 100^\circ\mathrm{C} \) and \( 125^\circ\mathrm{C} \) respectively. The heat current in \( CD \) is \( P \) watt. The value of \( P \) is _______.

A raindrop with radius \( R = 0.2 \, \text{mm} \) falls from a cloud at a height \( h = 2000 \, \text{m} \) above ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is:
[Density of water \( f_w = 1000 \, \text{kg m}^{-3} \), and Density of air \( f_a = 1.2 \, \text{kg m}^{-3} \), \( g = 10 \, \text{m s}^{-2} \) Coefficient of viscosity of air \( = 1.8 \times 10^{-5} \, \text{N s m}^{-2} \)]

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will:

If \( E \) and \( H \) represents the intensity of electric field and magnetising field respectively, then the unit of \( E/H \) will be:

In \( 5 \) minutes, a body cools from \( 75^\circ \text{C} \) to \( 65^\circ \text{C} \) at room temperature of \( 25^\circ \text{C} \). The temperature of body at the end of next \( 5 \) minutes is _______ \( ^\circ \text{C} \).

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JEE Main 2021 20th July Evening Shift

The length of a metal wire is \( l_{1} \) when the tension in it is \( T_{1} \) and is \( l_{2} \) when the tension is \( T_{2} \). The natural length of the wire is: