A simple pendulum of length $40$ cm subtends $60^{\circ}$ at the vertex in one full oscillation. What will be the shortest distance(in cm) between the initial position and the final position of the bob? ( between the extreme ends )

Open in App

Solution

Given,
$O A = O C =$ length of pendulum $= 40 c m, ∠ A O C = 60^{0}$

In triangle $O B C$ ,
$= 30^{0}$

Here, $O C = h y p o t e n u s e$

$A B = p e r p e n d i c u l a r$
$B C = b a s e$

We know,
$40 = 2 B C$
$B C = 20 c m$

Therefore,
$l e n g t h o f A C = 2 (B C)$

$= 2 (20) = 40 c m$

Therefore, the shortest distance between the initial position and the final position of the bob $= 40 c m$

Hence, this is the answer.

Suggest Corrections

Similar questions

Q. A simple pendulum executing

S H M

with a period of

6 s

between two extreme positions

B

and

C

about a point

O

. If the length of the arc

B C

10

cm, how long will the pendulum take the move from position

C

to a position

D

towards

O

exactly midway between

C

and

O

Q. A simple pendulum is moving simple harmonically with a period of 6 s between two extreme position B and C about a point O. If the angular distance between B and C is 10 cm, how long will the pendulum take to move from position C to a position D exactly midway between O and C

Q. If the bob of the simple pendulum moves from its mean position to one of its extreme positions then what fraction of the oscillation has it completed?

Q. A simple pendulum is oscillating with an angular amplitude

60^{\circ}

. The ratio of tensions in the string when the bob reaches the mean position and the extreme position respectively is :

Name the type of energy possessed by the bob of a simple pendulum when it is at (a) the extreme position,(b) the mean position, and (c) between the mean and extreme positions.

Join BYJU'S Learning Program

A simple pendulum of length 40cm subtends 60∘ at the vertex in one full oscillation. What will be the shortest distance(in cm) between the initial position and the final position of the bob? ( between the extreme ends )

A simple pendulum of length $40$ cm subtends $60^{\circ}$ at the vertex in one full oscillation. What will be the shortest distance(in cm) between the initial position and the final position of the bob? ( between the extreme ends )