A simple pendulum of length ' l ' has a brass bob attached at its lower end. It's period is ' T '. A steel bob of the 'same size, having density ' x ' times tha

Question

A simple pendulum of length ' l ' has a brass bob attached at its lower end. It's period is ' T '. A steel bob of the 'same size, having density ' x ' times that of brass, replaces the brass bob. Its length is then so changed that the period becomes ' 2 T '. What is the new length?

TestHub · Accepted Answer

The time period of a simple pendulum is given by $T = 2 π \frac{l}{g}$ .

The time period is independent of the mass, size, and density of the bob. Therefore, changing the material of the bob from brass to steel does not affect the time period.

Let the new length be $l^{'}$ . The new time period is given as $2 T$ .

$2 T = 2 π \frac{l ^{'}}{g}$

Substituting $T = 2 π \frac{l}{g}$ , we get:

$2 (2 π \frac{l}{g}) = 2 π \frac{l ^{'}}{g}$

$2 l = l^{'}$

Squaring both sides, we get:

$l^{'} = 4 l$

The new length of the pendulum is $4 l$ .

Answer: $4 l$

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