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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Laws of Motion

NEET 2012 · Physics · Laws of Motion

A car of mass 1000 ~kg negotiates a banked curve of radius 90 ~m on...

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

Options

  1. A20 ms−120 \mathrm{~ms}^{-1}
  2. B30 ms−130 \mathrm{~ms}^{-1}
  3. C5 ms−15 \mathrm{~ms}^{-1}
  4. D10 ms−110 \mathrm{~ms}^{-1}

Correct answer

B. 30 ms−130 \mathrm{~ms}^{-1}

Step-by-step solution

The angle of banking tan⁡θ=v2rg\tan \theta=\frac{v^2}{r g} Given, θ=45∘,r=90 m\theta=45^{\circ}, r=90 \mathrm{~m} and g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^2tan⁡45∘=v290×10v=90×10×tan⁡45∘\begin{aligned} \tan 45^{\circ} & =\frac{v^2}{90 \times 10} \\ v & =\sqrt{90 \times 10 \times \tan 45^{\circ}} \end{aligned}$SpeedofSpeed of\operatorname{car} v=30 \mathrm{~m} / \mathrm{s}$
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