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
$$\rho \left( h \right) = {\rho _0}{e^{ - {h \over {{h_0}}}}}$$, where $$\rho $$0 = 1.25 kg m−3
and
h0 = 6000 m, the value of N is _________.
Your input ____
2
JEE Advanced 2020 Paper 2 Offline
Numerical
+3
-1
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).
Your input ____
3
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A beaker of radius r is filled with water (refractive index $${4 \over 3}$$) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed $$\omega$$. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is h (h << H, h << r), as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature R. Which of the following is/are correct? (g is the acceleration due to gravity)
A
$$R = {{{h^2} + {r^2}} \over {2h}}$$
B
$$R = {{3{r^2}} \over {2h}}$$
C
Apparent depth of the bottom of the beaker is close to $${{3H} \over 2}\left( {1 + {{{\omega ^2}H} \over {2g}}} \right)^{-1}$$
D
Apparent depth of the bottom of the beaker is close to $${{3H} \over 4}{\left( {1 + {{{\omega ^2}H} \over {4g}}} \right)^{ - 1}}$$
4
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A student skates up a ramp that makes an angle 30$$^\circ$$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v0 and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)
A
$$v_0^2 - 2gh = {1 \over 2}gR$$
B
$$v_0^2 - 2gh = {{\sqrt 3 } \over 2}gR$$
C
the centripetal force required at points x and z is zero
D
the centripetal force required is maximum at points x and z
