21 The time period , T seconds, of a simple pendulum of length 7cm is given by the formula T=2pi sqrt ((l)/(g)) Katie uses a simple pendulum in an experiment to find an estimate for the value of g. Here are her results. l=52.0 correct to 3 significant figures. T=1.45 correct to 3 significant figures. Work out the upper bound and the lower bound for the value of g. Use pi =3.142 You must show all your working.

Question

Answer 1

The upper bound for the value of

is approximately

and the lower bound for the value of

is approximately

.

Answer 2

## Step 1:### The formula for the period

of a simple pendulum is given by

, where

is the length of the pendulum and

is the acceleration due to gravity.## Step 2:### To find

, we rearrange the equation to solve for

. Squaring both sides, we get:

### Simplifying, we obtain:

### Rearranging to solve for

, we get:

## Step 3:### Given

cm and

seconds, we first find the upper and lower bounds for

and

.### For

:#### The upper bound is

cm.#### The lower bound is

cm.### For

:#### The upper bound is

seconds.#### The lower bound is

seconds.## Step 4:### Calculate the upper bound for

using the lower bound of

and the upper bound of

:

## Step 5:### Calculate the lower bound for

using the upper bound of

and the lower bound of

:

## Step 6:### Perform the calculations:

Question