A solid circular disc (m, R) translates with V? and rotates with ω? = 2V₀/R at t = 0. Because of friction, pure rolling starts at t = t₀. The coefficient of friction is μ. Find t₀.

Option 1 -

V₀/(3μg)

Option 2 -

4V₀/(3μg)

Option 3 -

2V₀/(3μg)

Option 4 -

V₀/(μg)

10 Views | Posted 3 weeks ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

3 weeks ago

Correct Option - 1

Detailed Solution:

a = fr/m
∴ V = V? + at? = V? + (fr/m)t?
and α = 2Rfr/mR² = 2fr/mR
∴ ω = ω? - (2fr/mR)t?
∴ V = ωR ∴ v? + (fr/m)t? = ω? R - (2fr/m)t?
= (3fr/m)t? = V? = (fr/m)et?
∴ V = V? + V? /3 = 4V? /3
t? = mV? / (3μmg)
= V? /3μg

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