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Q. A frictionless wire $A B$ is fixed on a sphere of radius $R$. A very small spherical ball slips on this wire the time taken by this ball to slip from $A$ to $B$ is
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Motion in a Straight Line

Solution:

Acceleration of body along $A B$ is $g \cos \theta$
Distance travelled in time $t \sec =A B=\frac{1}{2}(g \cos \theta) t^{2}$
From $\Delta A B C, A B=2 R \cos \theta$
$2 R \cos \theta =\frac{1}{2} g \cos \theta t^{2} $
$t^{2} =\frac{4 R}{g}$
$t =2 \sqrt{\frac{R}{g}}$