Question 20N.3.SL.TZ0.c(i)

A student studies the relationship between the centripetal force applied to an object undergoing circular motion and its period $T$.

The object (mass $m$) is attached by a light inextensible string, through a tube, to a weight $W$ which hangs vertically. The string is free to move through the tube. A student swings the mass in a horizontal, circular path, adjusting the period $T$ of the motion until the radius $r$ is constant. The radius of the circle and the mass of the object are measured and remain constant for the entire experiment.

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The student collects the measurements of $T$ five times, for weight $W$. The weight is then doubled ($2W$) and the data collection repeated. Then it is repeated with $3W$ and $4W$. The results are expected to support the relationship

$W=\frac{4{\mathrm{\pi }}^{2}mr}{T^2}.$

In reality, there is friction in the system, so in this case $W$ is less than the total centripetal force in the system. A suitable graph is plotted to determine the value of $mr$ experimentally. The value of $mr$ was also calculated directly from the measured values of $m$ and $r$.