Question

two paticals are moving moving in ccirculaton cicular path os ame radii with angular speed 2rad/s and 4 rad/s the ratio of their centripetal acceleration​

Answer 1

Answer:

$\displaystyle{\dfrac{a_c}{a^{'}_c} =\dfrac{1}{4}}$

Explanation:

Given :

Two particles are moving in circular path of same radii .

Let say radius be R .

Angular speed are 2 rad / sec and 4 rad / sec .

We have to find ratio of centripetal acceleration​ .

We know :

Centripetal acceleration​ = Velocity square / Radius .

$\displaystyle{a_c=\dfrac{v^2}{R}}$

Now their ratio :

$\displaystyle{\dfrac{a_c}{a^{'}_c} =\dfrac{\dfrac{2^2}{R}}{\dfrac{4^2}{R}}}}\\\\\\\displaystyle{\dfrac{a_c}{a^{'}_c} =\dfrac{4}{16}}\\\\\\\displaystyle{\dfrac{a_c}{a^{'}_c} =\dfrac{1}{4}}$

Hence  ratio of their centripetal acceleration​ is 1 : 4 .

Answer 2

Answer:

${\pink{\green{\sf{\therefore Ratio=1:4}}}}$

Explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In the given question information given about two particles whose angular speed is given and radius of circular path is same(constant).

• So, we have to find the ratio of their centripetal acceleration.

$\underline \bold{Given : } \\ \bold{For \: First \: particle} \\ \implies Radius = constant = R\\ \implies Angular \: speed ( v_{1} ) = 2 \: rad /s \\ \bold{For \: Second \: particle} \\ \implies Radius = constant = R \\ \implies Angular \: speed( v_{2} ) = 4 \: rad /s \\ \\ \underline \bold{To \: Find : } \\ \implies Ratio \: of \: their \:centripetal \: acceleration = ?$

• According to given question :

• We know the formula of centripetal acceleration :

$\bold{By \:Using \: formula} \\ \implies Centripetal \: acceleration( a_{c}) = \frac{ {v}^{2} }{R} \\ \\ \bold{Ratio} \\ \implies \frac{ a_{c1} }{ a_{c2} } = \frac{ \frac{ { v_{1} }^{2} }{R} }{ \frac{ { v_{?} }^{2} }{R} } \\ \implies \frac{ a_{c1} }{ a_{c2} } = \frac{ { v_{1} }^{2} }{ v_{2}^{2} } \\ \implies \frac{ a_{c1} }{ a_{c2} } = \frac{ ({2})^{2} \times \frac{rad}{s} }{ ({4})^{2} \times \frac{rad}{s} } \\ \implies \frac{ a_{c1} }{ a_{c2} } = \frac{4}{16} \\ \implies \bold{\frac{ a_{c1} }{ a_{c2} } = \frac{1}{4} } \\ \\ \bold{\therefore Ratio \: of \: centripetal \: {acc}^{n} = 1 : 4}$