TS EAMCET · Physics · Gravitation
A meteor of mass ' \(m\) ' having a speed ' \(v\) ' at infinity reaches the surface of the earth with a speed of ( \(\mathrm{v}_{\mathrm{e}}\) is escape speed from the earth's surface)
- A \(\sqrt{2} \mathrm{v}_{\mathrm{e}}\)
- B \(\mathrm{v}_{\mathrm{e}}\)
- C \(2 \sqrt{v^2+v_e^2}\)
- D \(\sqrt{v^2+v_e^2}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{v^2+v_e^2}\)
Step-by-step Solution
Detailed explanation
Energy Conservation: \( \frac{1}{2}mv^2 + 0 = \frac{1}{2}mv_{surface}^2 - \frac{GM_e m}{R_e} \) \( v^2 = v_{surface}^2 - \frac{2GM_e}{R_e} \) Using \( v_e^2 = \frac{2GM_e}{R_e} \): \( v^2 = v_{surface}^2 - v_e^2 \) \( v_{surface}^2 = v^2 + v_e^2 \)…
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