Question

A race car moving on a circular track of radius 20 meters. If car’s speed is 108 km/h, then the magnitude of the centripetal acceleration is​

Answer 1

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A race car moving on a circular track of radius 20 meters. If car’s speed is 108 km/h, then the magnitude of the centripetal acceleration is​

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Given :-

A race car moving on a circular track of radius 20 metres.

Car's speed is 108 km/h.

To Find :-

What is the centrifugal acceleration.

Formula Used :-

Centrifugal Acceleration Formula :

$\longmapsto \sf \boxed{\bold{\pink{a_c =\: \dfrac{v^2}{r}}}}⟼ a c​ = rv 2$

$where,\sf a_ca c$

 = Centrifugal Acceleration

v = Velocity

r = Radius

Solution :-

Given :

$\leadsto⇝ Radius :\implies \sf\bold{\green{20\: metres}}⟹20metres\leadsto⇝ Velocity :\implies \sf 108\: km/h⟹108km/h\implies \sf 108 \times \dfrac{5}{18}⟹108× 185$

$\implies \sf \dfrac{\cancel{540}}{\cancel{18}}⟹ 18 540 ​ \implies \sf\bold{\green{30\: m/s}}⟹30m/s$

Hence, we get :

Radius (r) = 20 metres

Velocity (v) = 30 m/s

According to the question by using the formula we get,

$\dashrightarrow \sf a_c =\: \dfrac{(30)^2}{20}⇢a c​ = 20(30) 2$

$\dashrightarrow \sf a_c =\: \dfrac{30 \times 30}{20}⇢a c​ = 2030×30$

$\dashrightarrow \sf a_c =\: \dfrac{90\cancel{0}}{2\cancel{0}}⇢a c​ = 2 0​ 90 0$

$\dashrightarrow \sf a_c =\: \dfrac{\cancel{90}}{\cancel{2}}⇢a c​ = 2​ 90$

$\dashrightarrow \sf\bold{\red{a_c =\: 45\: m/s^2}}⇢a c​ =45m/s 2$

$\therefore∴$ The centrifugal acceleration is 45 m/s²