| Four balls each of radius 10 cm and mass 1 kg, 2 kg, 3 kg and 4 kg are attached to the periphery of massless plate of radius 1 m. What is moment of inertia of the system about the centre of plate? |
 |
A) \[8.08 kg/{{m}^{2}}\]
B) \[7.02 kg/{{m}^{2}}\]
C) \[10.04 kg/{{m}^{2}}\]
D) \[9.02 kg/{{m}^{2}}\]
Correct Answer: C
Solution :
| Moment of inertia of the system about the centre of plate is given by |
| \[I=\left[ \frac{2}{5}\times 1\times {{\left( 0.1 \right)}^{2}}+1\times {{\left( 1 \right)}^{2}} \right]+\left[ \frac{2}{5}\times 2\times {{\left( 0.1 \right)}^{2}}+2{{\left( 1 \right)}^{2}} \right]\] |
| \[+\left[ \frac{2}{5}\times 3\times {{\left( 0.1 \right)}^{2}}+3\times {{\left( 1 \right)}^{2}} \right]+\left[ \frac{2}{5}\times 4\times {{\left( 0.1 \right)}^{2}}+4\times {{\left( 1 \right)}^{2}} \right]\] \[=1.004+2.008+3.012+4.016\] |
| \[=10.04kg-{{m}^{2}}\] |
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