A toy car is moving on a circular path of radius 10 m on an inclined plane of inclination 30°. The coefficient of friction between the tyres and the inclined plane is μ=23. Find maximum constant speed of car such that car does not slip. Assume that the width of a car is negligible with respect to radius of circular path.

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Q.

A toy car is moving on a circular path of radius $10 m$ on an inclined plane of inclination $30 °$ . The coefficient of friction between the tyres and the inclined plane is $μ = \frac{2}{\sqrt{3}}$ . Find maximum constant speed of car such that car does not slip. Assume that the width of a car is negligible with respect to radius of circular path.

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a

$2 \sqrt{2} m / s$

b

$5 \sqrt{2} m / s$

c

$9 \sqrt{2} m / s$

d

$7 \sqrt{2} m / s$

answer is B.

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Detailed Solution

$From figure,$

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$f - mgsinθ = \frac{{mv}^{2}}{r}$

$μN - mgsinθ = \frac{{mv}_{\max}^{2}}{r}$

$μmgcosθ - mgsinθ = \frac{{mv}_{mas}^{2}}{r}$

$μgcosθ - gsinθ = \frac{v_{res}^{2}}{r} (here, θ = 30 °)$

$∴ v_{mat} = \sqrt{gr (μcosθ - sinθ)}$

$= \sqrt{gr (μcos 30 ° - \sin 30 °)}$

$= \sqrt{10 \times 10 (\frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{2} - \frac{1}{2})}$

$= \frac{10}{\sqrt{2}} = 5 \sqrt{2} m / s$

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A toy car is moving on a circular path of radius 10 m on an inclined plane of inclination 30°. The coefficient of friction between the tyres and the inclined plane is μ=23. Find maximum constant speed of car such that car does not slip. Assume that the width of a car is negligible with respect to radius of circular path.