An aircraft executes a horizontal loop of radius 1 km with a speed of 900 kmph. Then, the ratio of its centripetal acceleration to the acceleration due to gravity is:
Show Hint
- 6.38
- 3.19
- 12.76
- 5.38
The Correct Option is A
Solution and Explanation
Step 1: Convert speed to m/s and calculate centripetal acceleration.
Speed in m/s: \[ v = 900 \times \frac{1000}{3600} = 250 \, {m/s} \] Centripetal acceleration \( a_c \): \[ a_c = \frac{v^2}{r} = \frac{250^2}{1000} = 62.5 \, {m/s}^2 \] Step 2: Compare to gravitational acceleration.
Gravitational acceleration \( g \approx 9.81 \, {m/s}^2 \): \[ {Ratio} = \frac{a_c}{g} = \frac{62.5}{9.81} \approx 6.38 \]
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