Two substances $A$ and $B$ of equal mass $m$ are heated at uniform rate of $6\,cal\,s^{-1}$ under similar conditions. A graph between temperature and time is shown in figure. Ratio of heat absorbed $H_A/H_B$ by them for complete fusion is
$9/4$
$4/9$
$8/5$
$5/8$
If there are no heat losses, the heat released by the condensation of $x$ gm of steam at $100^o C$ into water at $100^o C$ can be used to convert $y$ gm of ice at $0^o C$ into water at $100^o C$. Then the ratio $y : x$ is nearly
A lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle, then the velocity of the bullet at the time of striking is ........ $m/s$ ($M.P.$ of lead $= 327\,^oC,$ specific heat of lead $= 0.03\,cal/g\,^oC,$ latent heat of fusion of lead $= 6\,cal/g$ and $J = 4.2\,joule/cal$ )
A rod of length $20 \,\,cm$ is made of metal. It expands by $0.075\,\, cm$ when its temperature is raised from $0^o C$ to $100^o C$. Another rod of a different metal $B$ having the same length expands by $0.045 cm$ for the same change in temperature, a third rod of the same length is composed of two parts one of metal $A$ and the other of metal $B$. Thus rod expand by $0.06 \,\,cm$.for the same change in temperature. The portion made of metal $A$ has the length .............. $cm$
A centigrade and a Fahrenheit thermometer are dipped in boiling water. The temperature is lowered until the Fahrenheit thermometer registers $140^o$ . ........ $^oC$ is the fall in temperature as registered by the Centigrade thermometer
A pendulum clock keeps correct time at $0\,^oC$. The thermal coefficient of linear expansion of the material of the pendulum is $\alpha $. If the temperature rises to $t\,^oC$, then the clock loses per day by (in second)