The potential energy of a point particle of mass $m$ undergoing rectilinear motion along the $x$-axis is given by

$$ V(x)=A x+B x^2 $$

What is the maximum speed attained by the particle if it starts from rest at $x=\frac{A}{B}$ ?

Two identical containers kept at the same temperature carry the same gas with different molecular mean free paths $l_1$ and $l_2$. The gas from the first container is completely transferred into the second at the same temperature. What is the molecular mean free path of the resultant mixture in the second container?

Consider the circuit with a Zener diode whose breakdown voltage $V_z=4 \mathrm{~V}$. What is the voltage $V_0$ if $V_i=20 \mathrm{~V}$ ?

Consider a mass-pulley system as shown in the figure. There is a wedge of mass $M$ and equal wedge angles $\theta$ lying on a rigid horizontal table. The coefficient of friction between the wedge and the table is $\mu$. There are two blocks of mass $m_1$ and $m_2$ lying on the incline of the wedge. The coefficients of friction between the blocks and wedge are $\mu_1$ and $\mu_2$ as shown in the figure. Consider $m_1>m_2$ and the coefficients of friction ( $\mu, \mu_1$ and $\mu_2$ ) to be less than $\tan \theta$. Gravity is acting downwards with acceleration due to gravity $g$. What should be the value of $\frac{m_1}{m_2}$ so that the system is in equilibrium?