Two circular discs of radius each 10 cm are joined at their centres...

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is

43 \times 10^{5}

dyne. cm, the angular acceleration of the discs about the given axis

A B

\_\_\_\_

\mathrm{rad} / \mathrm{s}^{2}

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown

Options

A11
B22
C100
D27

Correct answer

A. 11

Step-by-step solution

\alpha = \dfrac{\tau}{I}

I = \dfrac{1}{4}mR^2 + mR^2 + \dfrac{1}{4}mR^2 + m(2R)^2 + \dfrac{m(3R)^2}{12} + m\left(\dfrac{R}{2}\right)^2

= \left(\dfrac{3}{2} + 4 + 1\right)mR^2 = \dfrac{13}{2}mR^2 = \dfrac{13}{2} \times 600 \times 10^2 = 39 \times 10^4

\alpha = \dfrac{43 \times 10^5}{39 \times 10^4} \text{ rad/s}^2 = \dfrac{430}{39} \text{ rad/s}^2 \approx 11 \text{ rad/s}^2

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