2007 年

The voltage and the capacity of the cell of a portable music player are $3.6$ V and $700$ mA h respectively. The continuous playing time of the player is $15$ hours. The capacity $700$ mA h indicates the quantity of electric charges that the cell will discharge in $15$ hours of playing. Assume that the voltage remains constant during discharge, what is the estimated power of the player when it is playing ?

In the following circuit, three identical light bulbs are connected to a cell. Under what conditions will light bulb $P$ have the maximum brightness ?

Susan performs an experiment in which a radioactive source is placed closely in front of a GM counter. The graph shows the variation of count rate with time. What is the half-life of the radioactive substance ?

In the upper atmosphere, neutrons are produced by the action of cosmic rays. These neutrons interact with nitrogen nuclei as shown in the following reaction: ${}^{1}_{0}\mathrm{n}+{}^{14}_{7}\mathrm{N}\to X+{}^{1}_{1}\mathrm{H}$ Element $X$ will then emit a $\beta$ particle. The nuclear reaction is as follows : $X\to Y+{}^{0}_{-1}\beta$. What is the final product $Y$ ?

Some dangerous substances are stored in a metal container inside a wooden box as shown in the figure. What metal should be used for the container and what type of substance is stored ?

A body initially at rest, is exploded into two parts. Which of the following correctly describes the change in total momentum and total kinetic energy ?

Tom and John stand on two trolleys of negligible masses. Both boys are initially at rest and Tom holds a ball of $3$ kg. The masses of Tom and John are $30$ kg and $27$ kg respectively. After Tom has thrown the ball to John, Tom moves backwards with a speed of $1\ \mathrm{m\,s^{-1}}$. What is the speed of John after he has caught the ball ?

In the above figure, a $1$ kg block is suspended by a string under the ceiling. The block is pulled by a $3$ N horizontal force such that it makes angle $\theta$ to the vertical. Which of the following descriptions is correct ? (Note : The tension of the string is denoted as $T$.)

An electrical toy car of mass $m$ goes up an inclined plane of inclination $30^\circ$ with constant speed $v$. The air resistance acting on the car is half of the weight of the car. What is the average power of the car ?

A block of mass $1$ kg is sliding down with constant speed along an inclined plane of inclination $30^\circ$ to the horizontal. What are the gain in kinetic energy and the work done against friction by the block after travelling a distance of $2$ m along the plane ? (Take the acceleration due to gravity to be $10\ \mathrm{m\,s^{-2}}$.)