A frictionless wire AB is fixed on a sphere of radius R . A very small spherical ball slips on this

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2.Motion in Straight Line

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A frictionless wire $AB$ 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

A

$\frac{{2\sqrt {gR} }}{{g\cos \theta }}$

B

$2\sqrt {gR} .\frac{{\cos \theta }}{g}$

C

$2\sqrt {\frac{R}{g}} $

D

$\frac{{gR}}{{\sqrt {g\cos \theta } }}$

Solution

(c) Acceleration of body along $AB$ is $g\cos \theta $

Distance travelled in time $t\, sec $=$AB = \frac{1}{2}(g\cos \theta ){t^2}$

From $\Delta ABC,\;AB = 2R\cos \theta ;\;2R\cos \theta = \frac{1}{2}g\cos \theta {t^2}$

$⇒$ ${t^2} = \frac{{4R}}{g}$or $t = 2\sqrt {\frac{R}{g}} $

Standard 11

Physics

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