COMEDK · Physics · 6. Work Power Energy

A ball falls under gravity from a height of 10m with an initial downward velocity \(u\). It loses three-fifths (or 60%) of its energy in collision and then rises back to 5m. The initial velocity \(u\) is (\(g = 10 \text{ ms}^{-2}\))

A \(1\ ms^{-1}\)
B \(10\ ms^{-1}\)
C \(7.07\ ms^{-1}\)
D \(0.707\ ms^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(7.07\ ms^{-1}\)

Step-by-step Solution

Detailed explanation

Let the mass of the ball be \(m\) Initial total energy of the ball at height \(h_1 = 10\) is \(E_i = mgh_1 + \dfrac{1}{2}mu^2\) \(E_i = m(10)(10) + 0.5mu^2 = 100m + 0.5mu^2\) The ball loses \(60\%\) of its energy upon collision, so the remaining energy is \(0.4E_i\) The ball…

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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