Question

A pan with set of weights is attached with a light spring. When disturbed, the mass-spring system oscillates with a time period of 0.6s. When some additional weights are added then time period is 0.7s. The extension caused by the additional weights is approximately

• A. 1.38 cm
• B. 3.5 cm
• C. 1.75 cm
• D. 2.45 cm

Answer 1

The correct option is B 3.5 cm

b)2$\pi \sqrt{\frac{m}{k}}$=0.6....(i) and $2\pi \sqrt{\frac{m+m^{\prime }}{k}}=0.7...\left(ii\right)$

Dividing (ii) by (i) we get $(\frac{7}{6}{)}^2=\frac{m+m^{\prime }}{m}=\frac{49}{36}$
$\frac{m+m^{\prime }}{m}-1=\frac{49}{36}-1\Rightarrow \frac{m^{\prime }}{m}=\frac{13}{36}{m}^{\prime }\frac{13m}{36}$

Also$\frac{k}{m}=\frac{4{\pi }^2}{(0.6{)}^2}$
Desired extension = $\frac{m^{\prime }g}{k}$ = $\frac{13}{36}\times \frac{mg}{k}$
$\frac{13}{36}\times 10\times \frac{0.36}{4{\pi }^2}\approx 3.5cm$