One junction of a certain thermoelectric couple is at a fixed temperature $T_r$ and the other junction is at temperature $T$. The thermo-electromotive force for this is expressed by $E=k(T-T_r)[T_0-\frac{1}{2}(T+T_r)]$. At temperature $T=\frac{1}{2} T_0$,the thermoelectric power is

Perhydrol is an aqueous solution of

An object of mass $2m$ is projected with a speed of $100 \ m/s$ at an angle $\theta = \sin^{-1}(3/5)$ to the horizontal. At the highest point,the object breaks into two pieces of same mass $m$ and the first one comes to rest. The distance between the point of projection and the point of landing of the bigger piece (in metre) is (Given,$g = 10 \ m/s^2$)

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure). Through a hole of radius $r$ $(r << R)$ at its bottom,the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of the water stream when it hits the ground is $x$,then:

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ moving with velocity $v$ strikes the rod at one end perpendicular to the rod. After the collision,the particle comes to rest. The velocity of the centre of mass of the rod after the collision is:

Lichens indicate $SO_2$ pollution because they