Question 197: Waves

Question

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1
 and r2 . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be
5×10−4  s, the difference in radii, $$\left| {} \right.$$r1 $$-$$ r2 $$\left| {} \right.$$ is best given by :

Accepted Answer

The time period is given by the formula
$$T = 2\pi \sqrt {{l \over g}} $$
which clearly indicates that the time period is directly proportional to the length of the pendulum l, that is,
$$T \propto \sqrt l $$
Here, l = 1 m. Therefore,
$${{\Delta T} \over l} = {1 \over 2}{{\Delta l} \over l}$$ ....... (1)
where $$\Delta l = \left| {{r_1} - {r_2}} ight|$$. Substituting the values in Eq. (1), we get
$$5 	imes {10^{ - 4}} = {1 \over 2}\left( {{{{r_1} - {r_2}} \over 1}} ight)$$
$$ \Rightarrow {r_1} - {r_2} = 10 	imes {10^{ - 4}} = {10^{ - 3}}$$ m $$ = {10^{ - 1}}$$ cm $$ = 0.1$$ cm

Answer

1 cm

Answer

0.05 cm

Answer

0.5 cm

Answer

0.01 cm

Waves

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