A car of mass 100 kg is on a circular track of radius 10 m- and friction coefficient 0-6- It starts from rest and its speed increases at the rate of 2 m - s 2- what is the maximum speed it can have without slipping-A- None of theseB- 601-2 m - sC- 10001-4 m - sD- 32001-4 m - s

The correct option is D a_r=v^2/R, a_t 2m/s^2 both of which are caused by friction a_net=√(ar^2+a^2_t) =√(v^4/R^2+a_t^2) F_net=m a_net=f ⇒μ N = m √(v^4/R^2+a_ ...

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Byju's Answer

Standard XII

Physics

Static Friction

A car of mass...

Question

A car of mass 100 kg is on a circular track of radius 10m, and friction coefficient 0.6. It starts from rest and its speed increases at the rate of 2 m/s², what is the maximum speed it can have without slipping?

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None of these

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Solution

The correct option is B

$a_{r} = \frac{v^{2}}{R},$
$a_{t} - 2 m / s^{2}$
both of which are caused by friction
$a_{n e t} = \sqrt{a r^{2} + a_{t}^{2}}$
= $\sqrt{\frac{v^{4}}{R^{2}} + a_{t^{2}}}$
$F_{n e t} = m a_{n e t} = f$
$\Rightarrow μ N = m \sqrt{\frac{v^{4}}{R^{2}} + a_{t}^{2}} \Rightarrow (0.6) (100) (10) = 100 \sqrt{\frac{v^{4}}{R^{2}} + 4} \Rightarrow \frac{v^{4}}{R^{2}} = 32 \Rightarrow v = (3200)^{1 / 4} m / s$

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A car of mass 100 kg is on a circular track of radius 10m, and friction coefficient 0.6. It starts from rest and its speed increases at the rate of 2 m/s2, what is the maximum speed it can have without slipping?

The correct option is B ar=v2R, at−2m/s2 both of which are caused by friction anet=√ar2+a2t =√v4R2+at2 Fnet=manet=f ⇒μN=m√v4R2+a2t⇒(0.6)(100)(10)=100√v4R2+4⇒v4R2=32⇒v=(3200)1/4m/s

A car of mass 100 kg is on a circular track of radius 10m, and friction coefficient 0.6. It starts from rest and its speed increases at the rate of 2 m/s², what is the maximum speed it can have without slipping?