Principle Of Mathematical Induction

Question
CBSEENMA11014352

Find the angle in (a) radians (b) degrees through which a pendulum swings if its length is 75 cm and its tip describes an arc of length 21 cm.

Solution

Length of arc AB, l = 21 cm
Radius of pendulum, r = 75 cm
Using l over r space equals space straight theta comma we have straight theta space equals space open parentheses 21 over 75 close parentheses to the power of straight c
∴ (a) straight theta space equals space open parentheses 7 over 25 close parentheses to the power of straight c
(b) straight theta space equals space open parentheses 7 over 25 cross times 180 over straight pi close parentheses to the power of degree space equals space open parentheses 7 over 25 cross times 180 over 22 cross times 7 close parentheses to the power of degree equals open parentheses 882 over 55 close parentheses to the power of degree space equals 16 degree 2 apostrophe 11 apostrophe apostrophe
                                           

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