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A particle is kept at rest at the top of a sphere of diameter 42 m . When disturbed slightly, it slides down. At what height $h$ from the bottom, the particle will leave the sphere?
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Verified Answer
The correct answer is:
35 m
The condition of slipping by particle from top is given by
$\cos \theta=2 / 3$
From the figure,
$h=r \cos \theta=21 \times \frac{2}{3}=14 \mathrm{~m}$
Therefore, the required height at which the particle will leave the sphere is
$=21+h=21+14=35 \mathrm{~m}$
$\cos \theta=2 / 3$
From the figure,
$h=r \cos \theta=21 \times \frac{2}{3}=14 \mathrm{~m}$
Therefore, the required height at which the particle will leave the sphere is
$=21+h=21+14=35 \mathrm{~m}$
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