Question

Find the angle in radians through which a pendulum swings if its length is 75cm and the tip describes an arc length (1) 10cm

Answer 1

Hint: We know that the simple pendulum consists of a mass “m” from a string of length l and fixed at a pivot point “p”. When a certain external force is applied it moves back and forth with periodic motion. So it is displaced by a certain angle and it is found using the formula \[l=r\theta \]here l is arc length and “r” is radius or length of pendulum.

Complete step-by-step answer:
we know that the length of the arc is given by the formula \[l=r\theta \]
Here length of arc is l=10cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
Radius or length of pendulum is r=75cm. . . . . . . . . . . . . . . . . . . . . . . . . . (2)
Now we need to find the angle in radian or \[\theta \]
\[l=r\theta \]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)
\[10=75\times \theta \]
\[\theta =\dfrac{10}{75}\]
\[\theta =\dfrac{2}{15}radian\]
So, the angle by which pendulum swings is \[\theta =\dfrac{2}{15}radian\]
Note: In the length of the arc formula \[l=r\theta \]. The angle that pendulum swings obtained is in radians not in degrees. If in the question they ask to find the angle by which the pendulum swings in degrees then we have to convert radians to degrees. If we multiply the radians with \[\dfrac{180}{\pi }\]it converts to degrees.