Question

The time of oscillation of a pendulum varies as the square root of its length. if a pendulum of length 40 cm oscillates once in a second, then the length of the pendulum oscillating once in 2.5 seconds is:

Answer 1

answer will be 250cm

Answer 2

Given:

Time period of oscillation = square root of length

$T=\sqrt { L }$

$T=K\sqrt { L } .....(1)$

Where K is the proportionality constant in the equation.

Given $T_1 = 1 sec, L_1 = 40cm$

$[1]=K\sqrt { \left( 40 \right) }$        

$K=\frac { 1 }{ \sqrt { \left( 40 \right) } } ......(2)$

Also given, $T_2 = 2.5, L_2 = ?$

$T_{ 2 }=K\sqrt { L_{ 2 } }$

$2.5=\frac { 1 }{ \sqrt { \left( 40 \right) } } \times \sqrt { L_{ 2 } }$

Squaring on both the sides,

${ (2.5) }^{ 2 }=\frac { 1 }{ 40 } \times L_{ 2 }$

$6.25\times 40 = L_2$

$L_2 = 250cm$