2006 年

A substance $X$ is heated at a constant rate and its changing temperature over a time period is recorded. The data are plotted below.

Which of the following statements about the substance $X$ is incorrect ?

The initial temperature of a jar of juice is $80^\circ\mathrm{C}$ and the mass of the juice is $2$ kg. Susan adds ice cubes into the jar in order to cool down the juice to $20^\circ\mathrm{C}$. What is the minimum number of ice cubes at $0^\circ\mathrm{C}$ required ? (Neglect the heat capacity of the jar and assume there is no heat exchange with the surroundings.) Given : Mass of each ice cube $= 0.15$ kg Specific heat capacity of juice $= 4700\ \mathrm{J\,kg^{-1}\,{}^\circ C^{-1}}$ Specific heat capacity of water $= 4200\ \mathrm{J\,kg^{-1}\,{}^\circ C^{-1}}$ Specific latent heat of fusion of ice $= 3.34\times10^5\ \mathrm{J\,kg^{-1}}$

As shown above, an illuminated object is placed at a distance $20$ cm in front of a convex lens and a sharp image is formed on a screen at a distance of $16$ cm from the lens. The focal length of the convex lens is

A series of plane waves travel from medium $A$ into medium $B$. The figure above shows the positions, $PQ$ and $P^\prime Q^\prime$, of a wavefront before and after entering the medium $B$. What would happen to the speed and the wavelength of the wave when it travels from medium $A$ to medium $B$ ?

In December 2004, an earthquake in the Indian Ocean caused a tsunami which produced water waves having wavelength about $100$ m and frequency about $2$ Hz. What was the approximate time taken for these water waves to travel from the earthquake centre to Sri Lanka across a distance of about $1500$ km ?