NEETPhysicsCenter of Mass, Momentum and Collision
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Two identical particles start simultaneously from the same point on a smooth horizontal circular track and move in opposite directions with equal constant speeds. The magnitude of the acceleration of their center of mass is maximum at the instant they meet again. Reason (R): At the instant the part
Options
- ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
- BBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
- CAssertion (A) is true but Reason (R) is false
- DAssertion (A) is false but Reason (R) is true
Correct answer
B. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
Step-by-step solution
Let the particles start from = 0 and move with angular speed on a track of radius R . The position vectors of the two particles at time t are r ₁ = R ( t) i + R ( t) j and r ₂ = R ( t) i - R ( t) j . The position of the center of mass is r _ cm = m r ₁ + m r ₂ 2m = R ( t) i . The acceleration of the center of mass is a _ cm = d^2 r _ cm dt^2 = - ^2 R ( t) i . The particles meet again when they have each covered an angle of , i.e., t = . At this instant, the magnitude of the acceleration of the center of mass is | a