COMEDK · Physics · 4. Motion In Two Dimensions

A ball is moving in a circular path of radius \(5 \mathrm{~m}\). If tangential acceleration at any instant is \(10 \mathrm{~ms}^{-2}\) and the net acceleration makes an angle of \(30^{\circ}\) with the centripetal acceleration, then, the instantaneous speed is

A \(50 \sqrt{3} \mathrm{~ms}^{-1}\)
B \(5.4 \mathrm{~ms}^{-1}\)
C \(9.3 \mathrm{~ms}^{-1}\)
D \(6.6 \mathrm{~ms}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(9.3 \mathrm{~ms}^{-1}\)

Step-by-step Solution

Detailed explanation

The tangential acceleration is given as \(a_t = 10 \mathrm{~ms}^{-2}\). The centripetal acceleration is given by \(a_c = \dfrac{v^2}{r}\), where \(v\) is the instantaneous speed and \(r = 5 \mathrm{~m}\). Thus, \(a_c = \dfrac{v^2}{5}\). The net acceleration \(\vec{a}\) is the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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