Browse Questions

The length of string of a simple pendulum as measured by a meter scale was found to be 98.2cm. The diameter of the bob was measured by a vernier caliper and it was found to be 3.62cm. The time for 10 oscillations was found to be 21.2 seconds. What is maximum error in the value of g?

$\begin{array}{1 1}(A)\;1.04\% \\(B)\;1 \% \\(C)\;9.8\% \\(D)\;2 \% \end{array}$

$g= 4 \pi ^2 \large\frac{l}{T^2}$
$\bigg(\large\frac{\Delta g}{g}\bigg)_{max} $$\times 100 = \large\frac{\Delta l}{l}$$ \times 100 +\large\frac{2 \Delta T}{T} $$\times 100 T+\Delta T = \large\frac{t+ \Delta t}{n} T= \large\frac{t}{n} \large\frac{T+\Delta T}{T} = \frac{t+\Delta t}{t} \qquad= \large\frac{\Delta l}{l}$$ \times 100+ \large\frac{2 \Delta t}{t} $$\times 100 \qquad= \large\frac{0.1}{100 }$$ \times 100 +2 \times \large\frac{0.1}{21.2}$$\times 100$
$\qquad= 0.1 \% + 0.94 \%$
$\qquad= 1.04 \%$
Hence A is the correct answer.