Question:
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
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
Updated On: Jan 30, 2025
- $\frac{\sqrt{2gR}}{g\:cos\:\theta }\:$
- $\:2\sqrt{gR\:.}\:\frac{cos\:\theta }{g}$
- $\:2\sqrt{\frac{R}{g}}$
- $\:\frac{gR}{\sqrt{g\:cos\:\theta }}$
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The Correct Option is C
Solution and Explanation
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 $\triangle ABC , AB =2 R \cos \theta$
Thus, $2 R \cos \theta=\frac{1}{2} g \cos \theta t^{2}$
$\Rightarrow t^{2}=\frac{4 R}{g} \Rightarrow t=2 \sqrt{\frac{R}{g}}$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
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