A thin wire is bent into the shape of a parabola in the vertical plane as shown. A small bead ‘P’ can freely slide along the wire. The coefficient of friction between the bead and the wire is $' μ'$ . The condition on y so that the bead does not slip on the wire is :

see full answer

Want to Fund your own JEE / NEET / Foundation preparation ??

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

$y \leq 2 a μ$

$y \leq \frac{2 a}{μ}$

$y \geq \frac{2 a}{μ}$

$y \geq 2 a μ$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given
Coefficient of friction= $μ$
From diagram $y^{2} = 4 a x$
Differentiating on both sides
$2 y \frac{d y}{d x} = 4 a$
$\Rightarrow \frac{d y}{d x} = \frac{2 a}{y}$
For bead to be stationary, slope of tangent on the curve $\frac{d y}{d x} = \tan θ \leq μ$
$\Rightarrow \frac{2 a}{y} \leq μ$