The normal reaction N for a vehicle of 800kg mass, negotiating a...

The normal reaction

N

for a vehicle of

800kg

mass, negotiating a turn on a

30 °

banked road at maximum possible speed without skidding is ____

\times {10}^{3}kgm{s}^{- 2}

The normal reaction N for a vehicle of 800kg mass, negotiating a turn on a 30 ° banked road at maximum possible speed

Options

A $10 . 2$
B $7 . 2$
C $12 . 4$
D $6 . 96$

Correct answer

A. $10 . 2$

Step-by-step solution

The normal reaction N for a vehicle of 800kg mass, negotiating a turn on a 30 ° banked road at maximum possible speed

At ${v}_\max, f$ will be limiting in nature.

$∴$ Balancing force in vertical direction, $Ncos30 ° - mg - \mu Ncos60 ° = 0$
$⇒ N\left[\cos 30 ° - \mu cos60 °\right] = mg$
$∴ N = \dfrac{800 \times 10}{( 0 . 87 - 0 . 1 )} \approx 10 . 2 \times {10}^{3}kgm{s}^{- 2}$
Hence, option $1 .$

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