The $e.m.f.$ in a thermoelectric circuit with one junction at $0\,^\circ C$ and the other at $t\,^\circ C$ is given by $E = At - Bt^2$. The neutral temperature is then

One quality of a thermometer is that its heat capacity should be small. If $P$ is a mercury thermometer,$Q$ is a resistance thermometer,and $R$ is a thermocouple type,then:

$A$ metal rod is used as a pendulum. If the room temperature increases by $10^{\circ}C$ and the linear expansion coefficient of the metal is $2 \times 10^{-6} {\circ}C^{-1}$,then the percentage change in the time period of the pendulum is ...... $\%$

$1 \ gm$ of ice at $0^o C$ is mixed with $1 \ gm$ of steam at $100^o C$. What will be the final temperature $(^o C)$?

$10\, g$ of a lead bullet travelling at $300\, m/s$ strikes against a block of wood and comes to rest. Assuming $50\%$ of the heat produced is absorbed by the bullet,the increase in its temperature is ........ $^\circ C$. (Specific heat of lead $= 150\, J/kg\cdot K$)

$A$ bullet of mass $m$ moving with a uniform velocity $v$ stops suddenly after hitting a target. If the whole mass melts,given the specific heat $S$,initial temperature $25^{\circ}C$,melting point $475^{\circ}C$,and latent heat $L$,then $v$ is given by: