AP EAMCET · PHYSICS · Mathematics in Physics
Two intervals of time are measured as \(\Delta t_1=(2.00 \pm 0.02) \mathrm{s}\) and \(\Delta t_2=(4.00 \pm 0.02) \mathrm{s}\). The value of \(\sqrt{\left(\Delta t_1\right)\left(\Delta t_2\right)}\) with correct significant figures and error is
- A \((2.828 \pm 0.01) \mathrm{s}\)
- B \((2.83 \pm 0.01) \mathrm{s}\)
- C \((2.828 \pm 0.0075) \mathrm{s}\)
- D \((2.83 \pm 0.0075) \mathrm{s}\)
Answer & Solution
Correct Answer
(B) \((2.83 \pm 0.01) \mathrm{s}\)
Step-by-step Solution
Detailed explanation
Here, \(\Delta t_1=(2.00 \pm 0.02) \mathrm{s}\) and \(\Delta t_2=(4.00 \pm 0.02) \mathrm{s}\) Given, \(T=\sqrt{\left(\Delta t_1\right)\left(\Delta t_2\right)}=\sqrt{(2.00)(4.00)}=2.828427 \mathrm{~s}\) Now, according to the relative error of product…
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