Question

76.
Two cars are going round curves, one car travelling at 60 km/hr and the other at 30 km/hr. Each car experiences
the same centripetal acceleration. The radii of the two curves are in the ratio
14:1
(2) 2:1
(3) 1:2
(4) 1:4​

Answer 1

Answer:

OPTION 1 => 4:1

Explanation:

HEYA GM ❤

★ CENTRIPETAL ACCELERATION = V² / R

Now ;

→ V¹ ( Velocity of Car 1 ) = 60kmph

= 16.66 m/sec.

→ V² ( Velocity of Car 2) = 30kmph

= 8.33 m/sec.

★ RATIO OF RADII OF 2 CURVES :::::

»» (V¹)² / R¹ = (V²)² / R²

» ( 16.66 )² / R¹ = ( 8.33 ) ² / R²

» R¹ / R² = ( 16.66 )² / ( 8.33 )²

» R¹ / R² = 277.55 / 69.40

«★» R¹ / R² = 4 / 1 OR R¹ : R² = 4 : 1

=> Hence ; Ratio of Radius of Curves is 4 : 1.

Answer 2

» Two cars are going round curves, one car travelling at 60 km/hr and the other at 30 km/hr.

Here ...

• $V_{1}$ = 60 km/hr

=> 60 × $\frac{5}{18}$

=> 16.66 m/s

• $V_{2}$ = 30 km/hr

=> 30 × $\frac{5}{18}$

=> 8.33 m/s

____________ [ GIVEN ]

• We have to find the radii of the two curves in the ratio.

____________________________

We know that ..

${ V_{1}}^{2} { R_{1}} \:=\:{ V_{2}}^{2} { R_{2}}$

→ $\dfrac{( V_{1})^{2} }{ (V_{2})^{2} } \: = \: \dfrac{R_{1}}{R_{2}}$

→ $\dfrac{R_{1}}{R_{2}}$ = $\dfrac{ {(16.66)}^{2} }{ {(8.33)}^{2} }$

→ $\dfrac{R_{1}}{R_{2}}$ = $\dfrac{277.5556}{69.3886}$

=> $\dfrac{R_{1}}{R_{2}}$ = $\dfrac{4}{1}$

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4:1 is radii of the two curves.

_______ [ ANSWER ]

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