# Research between length and square of the time

Research question: – To find out if the length of the string holding the bob affects the gravitational force against the bob, i. e. the time period.

Hypothesis: – I think that the increase in the length of the string would result in the increase of the time period (time taken for one oscillation), Because The pendulum holding the longer string should take more time because it has a long way from starting to end point, whereas the pendulum with the short string would have a lesser distance to travel the length of the string is directly proportional to the time period, and the time period depends on the length of the string for one oscillation, keeping the mass of the bob constant. And the movement of the pendulum would be due to the gravitational force.

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Variables:- Independent Dependent Constant Length of the string Time period Mass of bob Manipulation of variables:- Independent:- Length- As the length increases the time period increases too, and as the length decreases the time period also decreases Dependent:- Time period- Is affected by the change in length, and is directly proportional to length Constant:- Mass of bob- is kept constant as the factor taken is the length Apparatus:- 1. String 2. Bob 3. Stop watch 4. Pendulum stand 5. Rubber split corks to hold string Method:- 1. First get all the materials needed 2. Then connect the string the rubber holder.

3. Connect it to the pendulum stand 4. Take out the string, which is put through the rubber and adjust the length. 5. Record the time taken for 10 oscillations for different lengths Data:- Length(cm) Time for 10 Oscillations(seconds) Time period(sec)(T) Trail 1 Trail 2 Trail 3 Average  Discussion of results:- As the shown on the graph the Time period2 increases as the length is increased.

There is also a steady increase, as a linear graph is formed as seen above. We can clearly see that the length is directly proportional to the time period. As I stated in my hypothesis, that the longer string has a longer distance to travel so it goes through more displacement and the tome period is increased Conclusion:- I conclude this experiment with the results which support my hypothesis, which said that as the length increases the time period for each length would increase and that the longer the length the more the time taken for 1 Oscillation.

Graph between length and square of the time period of a pendulum L and T2 plot is a straight line indicating that length is directly proportional to T2, Experimentally the value of the constant of Earth is found to be equal to 0. 248m/S2 and mathematically 0. 248 if found to be equal to Value of g (acceleration due to gravity) from the above relation we can derive a formula for time period This equation shows us the relation between time period and length in depth, and the formula can be tested, and using this formula, just substituting in the values would give you the needed value, for e.g. substituting values for G and pie and length we can find the time period.

Evaluation:- This experiment was successful and I think I could have done better if there was more time so that I could have taken more records for my data which would have made my results more accurate There were some human errors which were made during the experiment, for E. G. the length of the string measured by the ruler and then stuck between the rubber corks may not be so accurate and also the error made when we use the stop watch.