A person with his hand in his pocket is skating on ice at the rate of 10 ~m / s and describes a circle of radius 50 ~m . What is his inclination to vertical: (g=10 ~m / sec^ 2 )

BITSAT 2014

Exam: BITSAT
Year: 2014
Subject: Physics
Chapter: Laws of Motion

BITSAT 2014 · Physics · Laws of Motion

A person with his hand in his pocket is skating on ice at the rate...

A person with his hand in his pocket is skating on ice at the rate of

10 \mathrm{~m} / \mathrm{s}

and describes a circle of radius

50 \mathrm{~m}

. What is his inclination to vertical:

\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{sec}^{2}\right)

Options

A $\tan ^{-1}(1 / 2)$
B $\tan ^{-1}(1 / 5)$
C $\tan ^{-1}(3 / 5)$
D $\tan ^{-1}(1 / 10)$

Correct answer

B. $\tan ^{-1}(1 / 5)$

Step-by-step solution

Since surface (ice) is frictionless, so the centripetal force required for skating will be provided by inclination of boy with the vertical and that angle is given as

\tan \theta=\frac{\mathrmv^{2}}{\mathrm{rg}}

where

\mathrm{v}

is speed of skating

\

i is radius of circle in which he moves.

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