Centre of Mass & Rotational Motion · JEE Advanced previous year questions

2024 2 questions

1. Q222024 · 26 May 2024 · Paper 1· One or more correct

   A particle of mass $m$ is moving in a circular orbit under the influence of the central force $F(r)=-kr$, corresponding to the potential energy $V(r)=k{r}^2/2$, where $k$ is a positive force constant and $r$ is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by $L=n\hslash$, where $\hslash =h/(2\pi )$, $h$ is the Planck's constant, and $n$ a positive integer. If $v$ and $E$ are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

   1. A.$r^2=n\hslash \sqrt{\frac{1}{mk}}$
   2. B.$v^2=n\hslash \sqrt{\frac{k}{m^3}}$
   3. C.$\frac{L}{m{r}^2}=\sqrt{\frac{k}{m}}$
   4. D.$E=\frac{n\hslash }{2}\sqrt{\frac{k}{m}}$
   Show answer

   Answer: A, B, C

2. Q262024 · 26 May 2024 · Paper 1· Numerical answer
   
   Show answer

   Answer: 12