TS EAMCET · Physics · Gravitation

If a body is projected vertically from the surface of the earth with a speed of \(8000 \mathrm{~ms}^{-1}\), then the maximum height reached by the body is
(Radius of the earth \(=6400 \mathrm{~km}\) and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

A 1600 km
B 9600 km
C 6400 km
D 3200 km

Verified Solution

Answer & Solution

Correct Answer

(C) 6400 km

Step-by-step Solution

Detailed explanation

\(h = \frac{v^2 R}{2gR - v^2}\) \(h = \frac{(8000)^2 \times (6.4 \times 10^6)}{2 \times 10 \times (6.4 \times 10^6) - (8000)^2}\) \(h = \frac{64 \times 10^6 \times 6.4 \times 10^6}{128 \times 10^6 - 64 \times 10^6}\)…

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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If a body is projected vertically from the surface of the earth with a speed of \(8000 \mathrm{~ms}^{-1}\), then the maximum height reached by the body is(Radius of the earth \(=6400 \mathrm{~km}\) and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )

Step-by-step Solution

If a body is projected vertically from the surface of the earth with a speed of \(8000 \mathrm{~ms}^{-1}\), then the maximum height reached by the body is
(Radius of the earth \(=6400 \mathrm{~km}\) and acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )