A particle starts from rest and performing circular motion of constant radius with speed given by $v=\alpha \sqrt{x}$ where $\alpha$ is a constant and $x$ is the distance covered. The correct graph of magnitude of its tangential acceleration $\left(a_t\right)$ and centripetal acceleration $\left(a_c\right)$ versus $t$ will be

A particle of mass $m_1$ moves in a circular path of radius $R$ on a rotating table. A string connecting the particles $m_1$ and $m_2$ passes over a smooth hole made on the table as shown in figure. If mass $m_1$ does not slide relative to the rotating table, mark the correct option(s) as applicable.

Column I		Column II
	(i)
	(ii)
	(iii)
	(iv)
	(v)

Match the situation of the particle with the statement given in Column II.
 

 A particle $P$ of mass $m$ is attached to a vertical axis by two strings $AP$ and $BP$ of length $l$ each. The separation $AB=l$. $P$ rotates around the axis with an angular velocity $\omega$. The tensions in the two strings are $T_1$ and $T_2$. Choose the correct option(s).