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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 25th July Morning Shift

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: