Question

A pendulum of length 10 cm is hanged by wall making an angle 3° with vertical. It is swinged to position B. Time period of pendulum will be –

• A. p/5 sec
• B. $\frac { 2 \pi } { 15 }$ sec
• C. p/6 sec
• D. Subsequent motion will not be periodic

Answer 1

Answer: (B)

$\frac { 2 \pi } { 15 }$ sec

Answer 2

Time taken by pendulum in going from A to B

= $\frac { T } { 4 }$ where T = 2 $\sqrt { \frac { \ell } { \mathrm { g } } }$

Time taken by pendulum in going from B to C= $\frac { \mathrm { T } } { 12 }$

 Time period of pendulum

= $2 \left( \frac { T } { 4 } + \frac { T } { 12 } \right)$  $\frac { 2 \mathrm {~T} } { 3 }$ = $\frac { 2 } { 3 }$ . $\frac { \pi } { 5 }$ = $\frac { 2 \pi } { 15 }$ sec

Altier :

T = $\frac { 240 } { 360 }$ . T

= $\frac { 2 } { 3 } \mathrm {~T}$