$A$ particle is moving on a circular path of radius $r$ with uniform speed $v$. The change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = 40^\circ)$.

$50 \, g$ of copper is heated to increase its temperature by $10 \, ^\circ C$. If the same quantity of heat is given to $10 \, g$ of water,the rise in its temperature is ........ $^\circ C$. (Specific heat of copper $= 420 \, J \, kg^{-1} \, ^\circ C^{-1}$,Specific heat of water $= 4200 \, J \, kg^{-1} \, ^\circ C^{-1}$)

Which of the following compounds is consumed during the preparation of $Na_2CO_3$ by Solvay's process?

From a disc of radius $R$,a concentric circular portion of radius $r$ is cut out so as to leave an annular disc of mass $M$. The moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its centre of gravity is

Evaluate the sum: $\sum\limits_{k = 1}^n {\frac{1}{{{{\log }_{{2^k}}}(a)}}}$

In Earthworm,the dorsal wall of the intestine from the $26^{th}$ segment to the $95^{th}$ segment forms a median internal fold called: