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A car of mass 5 metric tons is moving up a smooth inclined plane with a velocity of $72 k m p h$ . If the power of the engine is $1500 k w$ , the angle of inclination of the inclined plane is $(g = 10 m s^{- 2})$

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$T a n^{- 1} (\frac{3}{2})$

$T a n^{- 1} (\frac{2}{3})$

$\sin^{- 1} (\frac{2}{3})$

$\sin^{- 1} (\frac{3}{2})$

answer is A.

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Detailed Solution

$(m g \sin θ) v = P$

$1500 \times 10^{3} = 5 \times 10^{3} \times 10 \times \sin θ \times (72 \times \frac{5}{18})$

$\Rightarrow 200 \sin θ = 300 \Rightarrow \sin θ = \frac{3}{2}$

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