Work, Energy and Power · Physics · IAT (IISER)

An object is released from rest from the inner edge of a hemispherical bowl, and it falls under gravity. The coefficient of kinetic friction between the object and the bowl is $\mu$. If the object covers an angular displacement $\theta$ with respect to the center of the hemisphere when it stops for the first time, which of the following expressions is correct?

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