First slide

Rectilinear Motion

Question

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

Moderate

A

$\frac{2 \sqrt{g R}}{g \cos θ}$
B

$2 \sqrt{g R}, \frac{\cos θ}{2}$
C

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

$\frac{g R}{\sqrt{g \cos θ}}$

Solution

Acceleration of body along AB is
$\begin{array}{l} Distance travelled in time t \sec = A B = \frac{1}{2} (g \cos θ) t^{2} \\ From Δ A B C, A B = 2 R \cos θ; 2 R \cos θ = \frac{1}{2} g \cos θ t^{2} \end{array}$
$\Rightarrow t^{2} = \frac{4 R}{g} or t = 2 \sqrt{\frac{R}{g}}$

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