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A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0.1 mole of an ideal gas at temperature 300 K. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in m) will be _______

(take the acceleration due to gravity = 10 ms−2 and the universal gas constant = 8.3 J mol−1K−1). Answer: 6 6x = 16... View Article

A point charge q of mass m is suspended vertically by a string of length l. A point dipole of dipole moment vector p is now brought towards q from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is × ( ℎ), where g is the acceleration due to gravity, then the value of N is _________ .

(Note that for three coplanar forces keeping a point mass in equilibrium, F/sin θ is the same for all forces, where F is any one of the... View Article

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of the density of air with height h from the ground is ρ(h) = ρ₀e^h/h0, where ρ₀ = 1.25 kg m^-3 and h_o = 6000 m, the value of N is ______.

Answer: 4 Applying equilibrium, ρ1vg = 480 g ρ2vg = (480 – N) g N = 480(1 – e(-1/120)) = 480(1 – 0.9917) = 4... View Article

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m⁻³ are released through a tiny hole at the centre of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a result, an oil drop of radius 8 × 10⁻⁷ m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is ________.

(neglect the buoyancy force, take acceleration due to gravity = 10 ms−2 and charge on an electron (e) = 1.6×10–19 C)... View Article

A train with cross-sectional area is moving with speed inside a long tunnel of cross-sectional area ₀ ( ₀= 4 ). Assume that almost all the air (density ρ) in front of the train flows back between its sides and the walls of the tunnel. Also, the airflow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be ₀. If the pressure in the region between the sides of the train and the tunnel walls is p, then p₀ – p = (7/2N) ρ v_t². The value of N is ________.

Answer: 9... View Article

A large square container with thin transparent vertical walls and filled with water (refractive index 4/3) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is ____________.

Answer: 2 or 3 For 2: We will assume that observer sees the image of object through edge. ⇒ α = 45° AB =... View Article

A circular disc of radius R carries surface charge density [latex]sigma (r) = sigma _{o}left ( 1-frac{r}{R} right )[/latex], where ₀ is a constant and r is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is ₀. Electric flux through another spherical surface of radius R/4 and concentric with the disc is . Then the ratio [latex]frac{phi_{o}}{phi }[/latex] is _________.

Answer: 6.4... View Article

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms⁻¹ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms⁻¹, the smallest value of the percentage change required in the length of the pipe is ____________.

Answer: 0.62 For open pipe resonance, f = nv / 4L Let us consider for n = 1, Initial length of pipe = L1 for f1 Now due to Doppler’s... View Article

Consider one mole of helium gas enclosed in a container at initial pressure ₁ and volume ₁. It expands isothermally to volume 4 ₁. After this, the gas expands adiabatically and its volume becomes 32 ₁. The work done by the gas during isothermal and adiabatic expansion processes are and , respectively. If the ratio / = fln2, then f is ________.

Answer: 1.77 Let the initial temperature be T For adiabatic process TV γ -1 = Constant, γ = 5 / 3 Wadb. = = =... View Article

One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0, 0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole pointing towards the charge q is fixed at the origin, the spring gets stretched to a length l and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by ∆ ≪ from its equilibrium position and released, it is found to oscillate at frequency [latex]frac{1}{delta }sqrt{frac{k}{m}}[/latex]. The value of δ is ______.

Answer: 3.14 As we know, for spring block system, , So we can also observe 'k' as from eq. So, we can say, The above... View Article

When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are 10³kg m⁻³, 0.07 Nm⁻¹ and 10 ms⁻², respectively, the value of h (in mm) is _________.

When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the... View Article

Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm and the right one at 90.00 cm. When you attempt to move both the fingers slowly towards the centre, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one start slipping. Then the right finger stops at a distance from the centre (50.00 cm) of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are 0.40 and 0.32, respectively, the value of (in cm) is ______.

Answer: 25.60 As the rod is in equilibrium ∴ netabout centre = 0 ∴ 50N1 = 40 N2 ∴ N2 > N1 ∴ by balancing... View Article

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO₄) of different concentrations ₁ and ₂( ₁> ₂) molecules per unit volume with ∆ = ( ₁− ₂) ≪ ₁. When they are connected by a tube of small length l and cross-sectional area S, KMnO₄ starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force − on each molecule, where β is a constant. Neglecting all terms of the order (∆ )², which of the following is/are correct? ( is the Boltzmann constant)

a) the force causing the molecules to move across the tube is ∆ b) force balance implies 1 = ∆ c) total number of molecules going... View Article

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity ρ. Its inner radius is R₁ and outer radius is R₂. If a voltage V₀ is applied between its two ends, a current I flows in it. In addition, it is observed that a transverse voltage ∆ develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then

a) b) the outer surface is at a higher voltage than the inner surface c) the outer surface is at a lower voltage than the inner surface d)... View Article

a uniform electric field E is applied in a region a charged particle of mass carrying positive charge is projected in this region with an initial speed of

a) the particle will hit T if projected at an angle 45o from the horizontal b) the particle will hit T if projected either at an angle 30o or... View Article

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [ ]; [speed] = [ ]; [acceleration] =[ ]; [linear momentum] = [ ]; [force] = [ ]. Then

a) α + = 2β b) + − = β c) − + = α d) + + = β Answer: a, b Position = [x ] ⇒... View Article

The filament of a light bulb has a surface area 64 mm². The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then

(Take Stefan-Boltzmann constant = 5.67 × 10−8 Wm−2K−4, Wien’s displacement constant = 2.90 × 10−3m-K,... View Article

A particle of mass m moves in circular orbits with potential energy V( ) = , where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle’s orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the n^th orbit (here h is the Planck’s constant)

Answer: b, c P.E., V(r) = Fr Therefore, Force = -dV/dr = – F F = mv2 / R …. (1) MvR = nh / 2 π ….. (2) From (2)... View Article

An open-ended U-tube of uniform cross-sectional area contains water (density 10³kg m⁻³). Initially, the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg m⁻³ is added to the left arm until its length is 0.1 m, as shown in the schematic figure below. The ratio h₂ / h₂ of the heights of the liquid in the two arms is

a) 15 / 14 b) 35 / 33 c) 7 / 6 d) 5 / 4 Answer: b ∵ Pressure will be same at same horizontal level, PA = PB (Same horizontal level)... View Article

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)

Answer: a Concept: based on Huygens’ principle. Theory of wavefront → wave moves such that direction of propagation is... View Article