Question

In the figure shown two identical disc of radius R, each are placed on a smooth horizontal plane. Thread unwraps without slack from discs when they move away from each other. At any instant acceleration of centre of disc A & B are a₂& a₁ respectively in opposite direction while their angular acceleration are a₂&a₁ respectively. If string unwraps from discs without slipping then –

• A. a₁ – Ra₁ = Ra₂ – a₂
• B. a₁ – a₂ = Ra₁ – Ra₂
• C. $\frac{d^{2}\mathcal{l}}{dt^{2}}$ = a₁ – a₂
• D. $\frac{d^{2}\mathcal{l}}{dt^{2}}$ = a₁ + a₂ – (Ra₁ + Ra₂)

Answer 1

Answer: (D)

$\frac{d^{2}\mathcal{l}}{dt^{2}}$ = a₁ + a₂ – (Ra₁ + Ra₂)

Answer 2

From constraint relation

$\frac{d^{2}\mathcal{l}}{dt^{2}}$ = (a₁ – Ra₁) + (a₂–Ra₂)