$A$ beaker is filled with water at $4\,^{\circ}C$. At one time the temperature is increased by a few degrees above $4\,^{\circ}C$ and at another time it is decreased by a few degrees below $4\,^{\circ}C$. One shall observe that:

  • A
    the level remains constant in each case
  • B
    in the first case water overflows while in the second case its level comes down
  • C
    in the second case water overflows while in the first case its level comes down
  • D
    water overflows in both the cases

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Fill in the blanks:
$(a)$ The $SI$ unit of the Stefan-Boltzmann constant is ...... .
$(b)$ In the thermal steady state of a rod,the temperature gradient is $5\,^{\circ}C/cm$ and the temperature of its hot end is $100\,^{\circ}C$. Then,at a distance of ........ $cm$ from the hot end,its temperature becomes $60\,^{\circ}C$.
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$A$ sphere of ice at $0^{\circ}C$ having initial radius $R$ is placed in an environment having ambient temperature $> 0^{\circ}C$. The ice melts uniformly,such that the shape remains spherical. After a time $t$,the radius of the sphere has reduced to $r$. Assuming the rate of heat absorption is proportional to the surface area of the sphere at any moment,which graph best depicts $r(t)$?

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