A block of mass 2M is attached to a massless spring with spring-constant k.This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a1, a2 and a3 as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x0. Which of the following option(s) is/are correct? [g is the acceleration due to gravity. Neglect friction]
A
$${a_2} - {a_1} = {a_1} - {a_3}$$
B
At an extension of $${{{x_0}} \over 4}$$ of the spring, the magnitude of acceleration of the block connected to the spring is $${{3g} \over {10}}$$.
C
$${x_0} = {{4Mg} \over k}$$
D
When spring achieves an extension of $${{{x_0}} \over 2}$$ for the first time, the speed of the block connected to the spring is $$3g\sqrt {{M \over {5k}}} $$
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle 60$$^\circ $$ with vertical? [g is the acceleration due to gravity]
A
The angular acceleration of the rod will be $${{2g} \over L}$$.
B
The normal reaction force from the floor on the rod will be $${{Mg} \over 16}$$.
C
The radial acceleration of the rod's center of mass will be $${{3g} \over 4}$$.
D
The angular speed of the rod will be $$\sqrt {{{3g} \over {2L}}} $$.
3
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $$\alpha $$ as shown in figure.
On the screen, the point O is equidistant from the slits and distance PO is 11.0 mm. Which of the following statement(s) is/are correct?
A
For $$\alpha $$ = 0, there will be constructive interference at point P.
B
For $$\alpha = {{0.36} \over \pi }$$ degree, there will be destructive interference at point P.
C
For $$\alpha $$ = $$\alpha = {{0.36} \over \pi }$$ degree, there will be destructive interference at point O.
D
Fringe spacing depends on $$\alpha $$.
4
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A free hydrogen atom after absorbing a photon of wavelength $$\lambda $$a gets excited from the state n = 1 to the state n = 4. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength $$\lambda $$e. Let the change in momentum of atom due to the absorption and the emission be $$\Delta {p_a}$$ and $$\Delta {p_e}$$, respectively. If $${{{\lambda _a}} \over {{\lambda _e}}} = {1 \over 5}$$, which of the option(s) is/are correct? [Use hc = 1242 eVnm; 1 nm = 10-9 m, h and c are Planck's constant and speed of light in vacuum, respectively]
A
The ratio of kinetic energy of the electron in the state n = m to the state, n = 1 is $${1 \over 4}$$
