Question

Two pendulums differ in lengths by 22 cm. They oscillate at the same place so that one of them makes 30 oscillations and the other makes 36 oscillations during the same time. The lengths (in cm) of the pendulums are

• A. 72 and 50
• B. 60 and 38
• C. 50 and 28
• D. 80 and 58

Answer 1

Answer: (A)

72 and 50

Answer 2

Time period of pendulum is

$\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm {~L} } { \mathrm {~g} } } \quad \therefore \frac { \mathrm {~T} _ { 1 } } { \mathrm {~T} _ { 2 } } = \sqrt { \frac { \mathrm { L } _ { 1 } } { \mathrm {~L} _ { 2 } } }$

Also, where and

$\therefore \sqrt { \frac { \mathrm { L } _ { 1 } } { \mathrm {~L} _ { 2 } } } = \frac { \mathrm { N } _ { 2 } } { \mathrm {~N} _ { 1 } } = \frac { 36 } { 30 }$ …… (i)

$\mathrm { L } _ { 1 } - \mathrm { L } _ { 2 } = 22 \mathrm {~cm}$ …… (ii)

Solving the Eqs. (i) and (ii), we get

cm and