$A$ body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The force on the body is $\frac{mv^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

Which bacteria can survive in water at temperatures exceeding $100 \, ^\circ C$?

The work function of a certain metal is $3.31 \times 10^{-19} \, J$. The maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength $5000 \, \text{Å}$ is: (Given: $h = 6.62 \times 10^{-34} \, J \cdot s$, $c = 3 \times 10^8 \, m/s$, $e = 1.6 \times 10^{-19} \, C$) (in $\text{eV}$)

If in a right-angled triangle $ABC$,the hypotenuse $AB = p$,then $\overrightarrow{AB} \cdot \overrightarrow{AC} + \overrightarrow{BC} \cdot \overrightarrow{BA} + \overrightarrow{CA} \cdot \overrightarrow{CB}$ is equal to

The number of points at which the function $f(x) = |x - 0.5| + |x - 1| + \tan x$ does not have a derivative in the interval $(0, 2)$ is:

$A$ line segment $l$ of length $a \ cm$ is rotated about a vertical line $L$ keeping the line $l$ in one of the following three positions: $(I)$ $l$ is parallel to $L$ and is at a distance of $r \ cm$ from $L$,$(II)$ $l$ is perpendicular to $L$ and its mid-point is at a distance $r \ cm$ from $L$,$(III)$ $l$ and $L$ are in the same plane and $l$ is inclined to $L$ at an angle $30^{\circ}$ with its mid-point at a distance $r \ cm$ from $L$. Let $A_1, A_2, A_3$ be the areas so generated. If $r > (a / 2)$,then