The pulley system shown in figure has a mass of 1.5 kg and a radius of gyration of 0.2 m. The angular acceleration of the pulleys, when the suspended masses are released is

F1 Engineering Arbaz 27-9-23 D13

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ISRO Scientist ME 2017 (II) Official Paper
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  1. 5 rad/sec2
  2. 10/1.3 rad/sec2
  3. 15/1.3 rad/sec2
  4. 10 rad/sec2

Answer (Detailed Solution Below)

Option 2 : 10/1.3 rad/sec2
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ISRO Scientist Mechanical FT 1
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Explanation:

Given, 

m1 = 1.5 kg k = 0.2 m

m2 = 1 kg m3 = 3 kg

r2 = 0.2 m r3 = 0.1 m

F1 Engineering Arbaz 27-9-23 D14

I1 = m1k2  

= 1.5 × 0.22  = 1 × 0.22

= 0.06 

\(\rm I_2 = m_2 r^2_2\) = 1 × 0.2= 0.04

\(\rm I_3 = m_3 r^2_3\)

= 3 × 0.12

= 0.03

(I1 + I2 + I3) α = m3gr3 - m2gr2

(0.06 + 0.04 + 0.03) α = 3 × 10 × 0.1 - 1 × 10 × 0.2

\(\alpha=\frac{1}{0.13}=\frac{10}{1.3} \mathrm{rad} / \mathrm{s}\)

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