JEE MAIN - Physics (2021 - 22th July Evening Shift - No. 20)
Three students S1, S2 and S3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.
(Least count of length = 0.1 cm and Least count for time = 0.1 s)
If E1, E2 and E3 are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no. ______________.
| Student No. |
Length of Pendulum (cm) |
No. of oscillations (n) |
Total time for n oscillations |
Time period (s) |
|---|---|---|---|---|
| 1 | 64.0 | 8 | 128.0 | 16.0 |
| 2 | 64.0 | 4 | 64.0 | 16.0 |
| 3 | 20.0 | 4 | 36.0 | 9.0 |
(Least count of length = 0.1 cm and Least count for time = 0.1 s)
If E1, E2 and E3 are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no. ______________.
Answer
1
Explanation
$$T = {t \over n} = 2\pi \sqrt {{l \over g}} $$
$$ \Rightarrow g = {{4{\pi ^2}l} \over {{T^2}}}$$
$$ \Rightarrow {{\Delta g} \over g} \times 100 = {{\Delta l} \over l} \times 100 + 2{{\Delta T} \over T} \times 100$$
$$ = \left( {{{\Delta l} \over l} + {{2\Delta T} \over {T}}} \right)100\% $$
$${E_1} = {{20} \over {64}}\% $$
$${E_2} = {{30} \over {64}}\% $$
$${E_3} = {{19} \over {18}}\% $$
$$ \Rightarrow g = {{4{\pi ^2}l} \over {{T^2}}}$$
$$ \Rightarrow {{\Delta g} \over g} \times 100 = {{\Delta l} \over l} \times 100 + 2{{\Delta T} \over T} \times 100$$
$$ = \left( {{{\Delta l} \over l} + {{2\Delta T} \over {T}}} \right)100\% $$
$${E_1} = {{20} \over {64}}\% $$
$${E_2} = {{30} \over {64}}\% $$
$${E_3} = {{19} \over {18}}\% $$
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