Question

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:

• A. 6.38
• B. 3.19
• C. 12.76
• D. 5.38

Hint:

Understanding the relationship between speed, radius, and centripetal force is crucial for solving problems involving circular motion.

Answer 1

The Correct Option is A

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 \( g \approx 9.81 \, {m/s}^2 \): \[ {Ratio} = \frac{a_c}{g} = \frac{62.5}{9.81} \approx 6.38 \]