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Physics Question on laws of motion

A car of mass 1000 kg1000 \,kg negotiates a banked curve of radius 90 m90\,m on a frictionless road. If the banking angle is 45∘45^{\circ}, the speed of the car is

A

20 ms−120\,ms^{-1}

B

30 ms−130 \,ms^{-1}

C

5 ms−15\, ms^{-1}

D

10 ms−110\, ms^{-1}

Answer

30 ms−130 \,ms^{-1}

Explanation

Solution

Here, m=1000 kg, R=90 m, θ=45∘m = 1000\,kg,\, R = 90 \,m,\, \theta = 45^{\circ}
For banking, tan⁡θ=v2Rg\tan \theta = \frac{v^2}{Rg}
or =v=Rgtan⁡θ = v = \sqrt {Rg \tan \theta }
=90×10×tan⁡45∘= \sqrt {90 \times 10 \times \tan 45^{\circ}}
=30, ms−1= 30,\ ms^{-1}