Question

A small sphere of mass $200$ gm is attached to an inextensible string of length $130$ cm whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius $50$ cm. Calculate the time period of this conical pendulum and the tension in the string. $({\pi }^2=10)$

Answer 1

$m=200g$

$l=130cm=1.3m$

So the time period of a pendulum doesn't depend on the mass of the Bob. It is equal to :

$2\pi \sqrt{l}\sqrt{g}$

where l is length and g is gravity. Which gives us:

$2t=\left(4{\pi }^2\right)\times \frac{1.3}{9.8}$ (squaring both sides)

${\pi }^{2}and9.8$ are approx the same so we can cut it out, giving us:

$\left(4\right)\times \left(1.3\right)=520s$

Therefore $2t=5.2s$

$t=2.29s$

the force on the string is simple $mg=\left(200\right)\times \left(10\right)=2000gm/s$