A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure.
When the distance of the piston from closed end is L = L0, the particle speed is v = v0. The piston is moved inward at a very low speed V such that $$V < < {{dL} \over L}{v_0}$$, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
A
After each collision with the piston, the particle speed increases by 2V.
B
If the piston moved inward by dL, the particle speed increases $$2v{{dL} \over L}$$.
C
The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from L0 to 1/2 L0.
D
The rate at which the particle strikes the piston is v/L.
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure.
Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3 m). If H1, H2, and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are
A
H2 > H1
B
H3 > H1
C
0.85 cm < (H2 $$ - $$ H1) < 0.9 cm
D
H2 > H3
3
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
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 $$3g\sqrt {{M \over {5k}}} $$
4
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 $$\sqrt {{{3g} \over {2L}}} $$.
