A particle describes a horizontal circle on the smooth surface of an inverted cone. The plane of that circle is at a height of 9.8cm above the vertex. Then the speed (in ms-1) of the particle is ................× 10

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A particle describes a horizontal circle on the smooth surface of an inverted cone. The plane of that circle is at a height of 9.8cm above the vertex. Then the speed (in ms^-1) of the particle is ................× 10^–2

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answer is 98.

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Detailed Solution

According to Newton law of motion

$Rcosθ = \frac{{mv}^{2}}{r} and Rsinθ = mg$

$r = htanθ = Radius of motion$

$r = htanθ = \frac{mg \cdot h}{\frac{{mv}^{2}}{r}} = \frac{rg.h}{v^{2}}$

$v = \sqrt{gh} = \sqrt{9.8 \times . 098} = 0.98 {ms}^{- 1}$

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