JEE (Advanced) 2020 Paper 2
Q.1 A large square container with thin transparent vertical walls and filled with water
4
(refractive index 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 ____________.
Q.2 A train with cross-sectional area 𝑆𝑡 is moving with speed 𝑣𝑡 inside a long tunnel of cross-sectional
area 𝑆0 (𝑆0 = 4𝑆𝑡 ). Assume that almost all the air (density ) in front of the train flows back between
its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar.
Take the ambient pressure and that inside the train to be 𝑝0 . If the pressure in the region between the
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sides of the train and the tunnel walls is 𝑝, then 𝑝0 − 𝑝 = 2𝑁 𝜌𝑣𝑡2 . The value of 𝑁 is ________.
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,JEE (Advanced) 2020 Paper 2
Q.3 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
center 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)
Q.4 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
ℎ
−
the density of air with height ℎ from the ground is 𝜌(ℎ) = 𝜌0 𝑒 ℎ0 , where 𝜌0 = 1.25 kg m−3 and
ℎ0 = 6000 m, the value of 𝑁 is _________.
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Q.5 A point charge q of mass 𝑚 is suspended vertically by a string of length 𝑙. A point dipole of dipole
moment 𝑝⃗ 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 𝑁 × (𝑚𝑔ℎ),
where g is the acceleration due to gravity, then the value of 𝑁 is _________ . (Note that for three
F
coplanar forces keeping a point mass in equilibrium, sin𝜃 is the same for all forces, where 𝐹 is any
one of the forces and 𝜃 is the angle between the other two forces)
Q.6 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−1 K −1).
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Q.1 A large square container with thin transparent vertical walls and filled with water
4
(refractive index 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 ____________.
Q.2 A train with cross-sectional area 𝑆𝑡 is moving with speed 𝑣𝑡 inside a long tunnel of cross-sectional
area 𝑆0 (𝑆0 = 4𝑆𝑡 ). Assume that almost all the air (density ) in front of the train flows back between
its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar.
Take the ambient pressure and that inside the train to be 𝑝0 . If the pressure in the region between the
7
sides of the train and the tunnel walls is 𝑝, then 𝑝0 − 𝑝 = 2𝑁 𝜌𝑣𝑡2 . The value of 𝑁 is ________.
1/9
,JEE (Advanced) 2020 Paper 2
Q.3 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
center 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)
Q.4 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
ℎ
−
the density of air with height ℎ from the ground is 𝜌(ℎ) = 𝜌0 𝑒 ℎ0 , where 𝜌0 = 1.25 kg m−3 and
ℎ0 = 6000 m, the value of 𝑁 is _________.
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, JEE (Advanced) 2020 Paper 2
Q.5 A point charge q of mass 𝑚 is suspended vertically by a string of length 𝑙. A point dipole of dipole
moment 𝑝⃗ 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 𝑁 × (𝑚𝑔ℎ),
where g is the acceleration due to gravity, then the value of 𝑁 is _________ . (Note that for three
F
coplanar forces keeping a point mass in equilibrium, sin𝜃 is the same for all forces, where 𝐹 is any
one of the forces and 𝜃 is the angle between the other two forces)
Q.6 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−1 K −1).
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