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 $${{3H} \over 4}{\left( {1 + {{{\omega ^2}H} \over {4g}}} \right)^{ - 1}}$$
2
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
3
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
A rod of mass m and length L, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now rotates with angular speed $$\omega$$ about the pivot. The maximum angular speed $$\omega$$M is achieved for x = xM. Then
A
$$\omega = {{3vx} \over {{L^2} + 3{x^2}}}$$
B
$$\omega = {{12vx} \over {{L^2} + 12{x^2}}}$$
C
$${x_M} = {L \over {\sqrt 3 }}$$
D
$${\omega _M} = {v \over {2L}}\sqrt 3 $$
4
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to $${1 \over 2}$$, the potential difference V is increased to 2V, and the separation distance d is reduced to $${d \over 2}$$, then
A
the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the same
B
the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same
C
the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease
D
the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease
