Q. 135.0( 3 Votes )

# Two cars having masses m1 and m^{2} move in circles of radii r_{1} and r_{2} respectively. If they complete the circle in equal time. What is the ratio of their speeds and centripetal accelerations?

Answer :

According to the question given that;

Mass of first car = m_{1}.

The radius of first car = r_{1}.

Mass of second car = m_{2}.

The radius of second car = r_{2}.

Now let;

The speed of first car = V_{1}.

The speed of second car = V_{2}.

Time is taken for the first car to complete = T_{1} =

Time is taken for the second car to complete = T_{2} = _{.}

According to question;

T_{1} = T_{2}.

⇒ _{.}

⇒

⇒ .

Hence the ratio of speeds is .

Centripetal acceleration of First car a_{1} =

Centripetal acceleration of Second car a_{2} =

⇒

⇒

⇒

⇒

Hence the ratio of centripetal acceleration is

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