Question

7.
Find the angle in radian through which a pendulum swings if its length is 75 cm
and the tip describes an arc of length
(i) 10 cm
(ii) 15 cm (iii) 21 cm​

Answer 1

$\bf{}Here \: we \: go!!$

TOPIC:-

=>Trigonometry

GIVEN:-

=>Length of the pendulum is 75cm.

TO FIND:-

=>The angle in radian through which a pendulum swings.

$\bf{}Understanding \: The \: Concept$

According to the question,

=>We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then,

$\bf{θ = \dfrac{1}{r} }$

So, it is already given that length as 75cm that is nothing but radius.

ANSWER:-

$\bf{1)l = 10cm}$

$\bf{θ = \dfrac{10}{75} = > \dfrac{2}{15} radian}$

$\bf{2)l = 15cm}$

$\bf{θ = \dfrac{15}{75} = > \dfrac{1}{5} \: radian}$

$\bf{3) \: l = 21cm}$

$\bf{θ = \dfrac{21}{75} = > \dfrac{7}{25} radian}$

=>Therefore, the angle in radian are,

$\bf{ \dfrac{2}{15} , \dfrac{1}{5} , \dfrac{7}{25} .}$