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 0.6 s. When some additional weights are added then time period is 0.7s. The extension caused by the additional weights is approximately given by

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

Answer 1

Answer: (B)

3.5 cm

Answer 2

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

Dividing (ii) by (i) we get

$\left( \frac { 7 } { 6 } \right) ^ { 2 } = \frac { m + m ^ { \prime } } { m } = \frac { 49 } { 36 }$ $\frac { m + m ^ { \prime } } { m } - 1 = \frac { 49 } { 36 } - 1 \Rightarrow \frac { m ^ { \prime } } { m } = \frac { 13 } { 36 }$

⇒ $m ^ { \prime } = \frac { 13 m } { 36 }$

Also $\frac { k } { m } = \frac { 4 \pi ^ { 2 } } { ( 0.6 ) ^ { 2 } }$

Desired extension $= \frac { m ^ { \prime } g } { k }$ $= \frac { 13 } { 36 } \times \frac { m g } { k }$

$= \frac { 13 } { 36 } \times 10 \times \frac { 0.36 } { 4 \pi ^ { 2 } } \approx 3.5 \mathrm {~cm}$