IAT IISER 2020

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?

$$\text { Match the human cell types or (column I) to the number of chromatids (column II) }$$

\(\text { The number of unpaired electron(s) in the square planar complex }[\text{Ni}(\text{CN})_4]^{2-} \text { is/are }\) :

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 $x=\frac{A}{B}$ ?