A 2.5 V battery is connected to a potentiometer wire. A cell of e.m.f. 1.08 V is balanced by the voltage drop across 2.16 m of wire. The length of the potentiometer wire is

A stone of mass ' m ' kg is tied to a string of length ' $L$ ' $m$ and moved in a vertical circle of radius 49 cm in a vertical plane. If it completes 30 revolutions per minute, the tension in the string when it is at the lowermost point is nearly [Take $\pi^2=10$ and acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]

A photosensitive surface has work function $\phi$. If photon of energy $3 \phi$ falls on this surface, the electron comes out with maximum velocity of $4 \times 10^6 \mathrm{~m} / \mathrm{s}$ When photon energy is increased to $7 \phi$ then maximum velocity of photoelectron will be

A vessel completely filled with water has two holes ' P ' and ' Q ' at depths ' 2 h ' and ' 8 h ' from the top respectively. Hole ' P ' is square of side ' $a$ ' and hole ' $Q$ ' is a circle of radius ' $r$ '. The water flowing out per second from both the holes is same, then side ' $a$ ' of hole ' $P$ ' is