Constants of motion – Page 2

Physics concepts and problems for the JEE

Mirror on a spring

January 19th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 12

A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular frequency $\Omega$ such that $\frac{4 \pi M \Omega}{h} = 10^{24} \, {\rm m}^{-2}$ with $h$ as Planck’s constant. $N$ photons of wavelength $\lambda = 8 \pi \times 10^{-6} \, {\rm m}$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1 \mu{\rm m}$ .
If the value of $N$ is $x \times 10^{12}$ , what is the value of $x$ ?

[Consider the spring as massless]

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Solution

The momentum carried by a single photon is given by the de Broglie relation $p_{\rm ph} = h/\lambda$ . The total momentum carried by $N$ photons is therefore $N \times p_{\rm ph} = Nh/\lambda$ . All the photons hit the mirror simultaneously and are reflected …

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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