In the figure given below, an ideal pendulum oscillates in vacuum between two extreme positions $A$ and $B$ . If it goes from position $A$ to position $B$ and then returns from position $B$ to mean position $C$ in $3 s$ , then it will complete $3.5$ oscillations in

14 s

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4 s

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1.14 s

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2 s

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Solution

The correct option is A $14 s$
Given that from A to B & then B to the pendulum takes $3 s e c$ .
during one oscillation will move from C to B then B & C then C to A and A to C
$\Rightarrow$ Time taken to trans T
as time taken to travels C to B $= \frac{T}{4}$
$a r c (A C = C B)$
$\Rightarrow$ time taken to travels from A to B
$= \frac{T}{4} \times 2 = \frac{T}{2}$
Time taken to travel from B to C = $\frac{T}{4}$
Now given that
$\frac{T}{2} + \frac{T}{4} = 3 s e c$
$\Rightarrow T = 4 s e c$
= time period of on oscillation $= 4 s e c$
= time period of $3.5$ oscillation
$= 3.5 \times 4 = 14 s e c$ .

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In the figure given below, an ideal pendulum oscillates in vacuum between two extreme positions A and B. If it goes from position A to position B and then returns from position B to mean position C in 3 s, then it will complete 3.5 oscillations in

In the figure given below, an ideal pendulum oscillates in vacuum between two extreme positions $A$ and $B$ . If it goes from position $A$ to position $B$ and then returns from position $B$ to mean position $C$ in $3 s$ , then it will complete $3.5$ oscillations in