Question

4. Prove that:

(a) sin A = 3sin
(A/3)-
4sin^3
(A/3)​

Answer 1

$\red\bigstar\:\:{\boxed{\boxed{\bf{\color{coral}Centripetal\:acceleration\:\atop{\color{coral}remains \:unchanged\:}}}}}$

$\Large{\underline{\underline{\bf{\color{cyan}EXPLANATION}}}}$

$\bf\blue{We\:know\:that}$

$\pink\bigstar\:\:\bf\green{Centripetal\:acceleration\:(a_c)\:=\:{\omega}^2\:{r}}$

$\bf{\color{olive}Where,}$

ω = Angular velocity

$:\implies\:\:\bf{a_c\:=\:\omega\:.\:\omega{r}}$

$\bf\purple{As,}$

$\longmapsto\:\:\bf\red{v\:=\:\omega{r}\:}$

$\bf\pink{Where,}$

v = Orbital speed

r = radius of orbit

$\bf\green{So,}$

$:\implies\:\:\bf{a_c\:=\:\omega\:v}--(1)$

$\bf\red{According \:to\:question,}$

$\checkmark\:\:\bf{v\:\longrightarrow\:v'\:=\:2v\:}$

$\checkmark\:\:\bf{\omega\:\longrightarrow\:{\omega}'\:=\:\dfrac{\omega}{2}\:}$

$\bf\orange{Hence,}$

$:\implies\:\:\bf{a'_c\:=\:{\omega}'\:v'}$

$:\implies\:\:\bf{a'_c\:=\:\dfrac{\omega}{2}\times{2v}\:}$

$:\implies\:\:\bf{a'_c\:=\:{\omega}\:v\:}$

$:\implies\:\:\bf{\color{peru}a'_c\:=\:a_c\:}\:[from\:equ^n(1)]$

$\Large\bf\purple{Therefore,}$

☆ New centripetal acceleration is equal to the initial centripetal acceleration.

$\Large\bf\red{So,}$

✔ Centripetal acceleration is unchanged.

Answer 2

Step-by-step explanation:

V= orbital apeed

R= radius of orbit