Uniform Circular Motion: Practice Problem & Solution
Assertion (A): Two identical trains move in opposite sense in equatorial plane with equal speed relative to earth's surface. They have equal magnitude of normal reaction. Reason (R): The trains require same centripetal force although they have different speeds.
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Uniform Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:
The absolute speed of the trains relative to Earth's center is \( v_{\text{abs}} = R_E \omega_E pm v_{\text{surface}} \). Since their absolute speeds are different, the centripetal force required \( F_c = m v_{\text{abs}}^2 / R_E \) will be different. The normal reaction is \( N = mg - F_c \), so it will also be different. Therefore, both Assertion (A) and Reason (R) are false.
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