A) \[-45.5\text{ }rad/{{s}^{2}}\]
B) \[-33.5\text{ }rad/{{s}^{2}}\]
C) \[-29.5\text{ }rad/{{s}^{2}}\]
D) \[-25.5\text{ }rad/{{s}^{2}}\]
Correct Answer: D
Solution :
Here: Speed of car = 72 km/hr \[=\frac{72\times 5}{18}=20cm/s\] Diameter of each wheel\[=\frac{0.5}{2}m\] Number of rotation = 20 The relation for angular speed is \[\omega =\frac{\upsilon }{r}=\frac{20}{0.25}=80\,rad/\sec \] Angular displacement \[Q=2\pi \times 20=40\text{ }\pi \text{ }rad\] The relation for angular retardation is given by \[{{\omega }^{2}}=\omega _{0}^{2}+2aQ\] \[0={{(80)}^{2}}+2a(40\pi )\] Or \[a=\frac{{{(80)}^{2}}}{80\pi }=-25.5\,rad/{{s}^{2}}\]
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