Question

A bead of mass m is free to move along a fixed and smooth parabolic wire of shape y = x2. Bead is released fromheight H from rest, when height of bead from ground is then for that moment choose the correct options :(1) Speed of bead is gH​

Answer 1

Answer:

here is your answer

Answer 2

Concept:

• Parabolic curves
• Tangential forces

Given:

• a bead of mass m free to move on a parabolic wire
• shape of parabolic wire y = x^2
• Bead is released from a height H

Find:

• Tangential acceleration when y = 1

Solution:

Equation of parabola x^2 = 4ay

Tangential force = mg cos α where α is the angle between the bead and the horizontal

F = mg cos α

a = g cos α

a = g cos (90-β) where β is the angle between the bead and the gravitational force

a = g sin β

tan β = dy/dx

x^2 = 4ay

(d/dx) x^2 = 4a dy/dx

2x = 4a dy/dx

x = 2a dy/dx

dy/dx = x/2a

y = 1 = a

x^2 = 4a^2

x = 2a

dy/dx = 1 = tan β

β = 45°

a = g sin β

a = g sin 45°

a = g/√2

Tangential acceleration when y = 1 is g/√2.

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