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, | r1 - r2| is best given by :

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, | r1 - r2| is best given by : (A) 1 cm (B) 0.1 cm (C) 0.5 cm (D) 0.01 cm

Tardigrade Admin · Accepted Answer

T propto √l l=1 (Δ T/l)=(1/2) (Δ l/l) Δ l=r1-r2 5×10-4=(1/2) (r1-r2/1) r1-r2=10×10-4 10-3 m=10-1 cm-0.1 cm

1 cm

0.1 cm

0.5 cm

0.01 cm

T∝l​l=1 lΔT​=21​lΔl​Δl=r1​−r2​ 5×10−4=21​1r1​−r2​​ r1​−r2​=10×10−4 10−3m=10−1cm−0.1cm

$T \propto l l = 1$
$\frac{Δ T}{l} = \frac{1}{2} \frac{Δ l}{l} Δ l = r_{1} - r_{2}$
$5 \times 1 0^{- 4} = \frac{1}{2} \frac{r _{1} - r _{2}}{1}$
$r_{1} - r_{2} = 10 \times 1 0^{- 4}$
$1 0^{- 3} m = 1 0^{- 1} c m - 0.1 c m$