jeefirst – Page 8

Particle in a tube

January 16th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 3

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 the closed end is $L=L_{0}$ the particle speed is $v=v_{0} .$ The piston is moved inward at a very low speed $V$ such that $V \ll \frac{{\rm d} L}{L} v_{0}$ , where ${\rm d} L$ is the infinitesimal displacement of the piston. Which of …

An infinite ladder of resistors

January 16th, 2022jeefirst0 Comments

Problem 3.152 of Irodov

The figure below shows an inifite circuit formed by the repetition of the same link, consisting of resistance $R_1 = 4.0 \ \Omega$ and $R_2 = 3.0 \ \Omega$ . Find the resistance of this circuit between points $A$ and $B$ .

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Solution

Let’s denote the resistance between the points $A$ and $B$ by $R_{AB}$ . Since the circuit is infinite, removing the first $R_1$ and $R_2$ resistors gives the same arrangement back again — the arrangement is self-similar. That means, the resistance between the points $C$ and $D$ is just $R_{AB}$ without the left-most $R_1$ and $R_2$ resistors, and we may redraw the circuit as shown below.

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It is now straightforward to calculate the resistance,

(1) …

Pulleys and masses connected to a spring

January 14th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 2

A block of mass $2 M$ is attached to a massless spring with spring-constant $k$ . This block is connected to two other blocks of masses $M$ and $2 M$ using two massless pulleys and strings. The accelerations of the blocks are $a_{1}, a_{2}$ and $a_{3}$ 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 $x_{0}$ . Which of the following option(s) is/are correct?

[ $g$ is the acceleration due to gravity. Neglect friction]

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$x_{0}=\frac{4 M g}{k}$
When spring achieves an extension of $\frac{x_{0}}{2}$ for the first time, the speed of the

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A falling rod

January 11th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 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]

The angular speed of the rod will be $\sqrt{\frac{3 g}{2 L}}$
The angular acceleration of the rod will be $\frac{2 g}{L}$
The radial acceleration of the rod’s center of mass will be $\frac{3 g}{4}$
The normal reaction force from the

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Infinitely bouncing ball

January 10th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 9

A ball is thrown from ground at an angle $\theta$ with horizontal and with an initial speed $u_{0}$ . For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $V_{1}$ . After hitting the ground, the ball rebounds at the same angle $\theta$ but with a reduced speed of $u_{0}/\alpha$ . Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $0.8 V_{1}$ , what is the …