Question

Three simple pendulums have lengths of strings $49cms,48cms$ and $47cms$ with diameters of the bobs $2cms,4cm$ and $6cm$ respectively. Then their periods are in the ratio:

• A. $1:1:1$
• B. $1:2:3$
• C. $3:2:1$
• D. $51:52:53$

Answer 1

The correct option is A $1:1:1$

$e=e\left(string\right)+r\left(radiosofthebob\right)$
$e_1=49-1$ $=50cm$
$e_2=(48+2)$ = 50 cm
$e_3=(47+3)$ = 50
$\therefore T=2\pi \sqrt{\frac{e}{g}}$
$\therefore 2\pi \sqrt{\frac{50}{g}}:2\pi \sqrt{\frac{50}{g}}:2\pi \sqrt{\frac{50}{g}}$

$1:1:1$