JEE Mains · Physics · STD 11 - 7. gravitation
To project a body of mass \(m\) from earth's surface to infinity, the required kinetic energy is _______. (assume, the radius of earth is \(R_E, g=\) acceleration due to gravity on the surface of earth)
- A \(2 \mathrm{mgR}_{\mathrm{E}}\)
- B \(m g R_E\)
- C \(\frac{1}{2} \mathrm{mgR}_{\mathrm{E}}\)
- D \(4 \mathrm{mgR} R_E\)
Answer & Solution
Correct Answer
(B) \(m g R_E\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{2} \mathrm{mv}_{\mathrm{e}}^2=\frac{\mathrm{GMm}}{\mathrm{R}_{\mathrm{E}}}\) \(\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}_{\mathrm{E}}^2}\) \(\mathrm{~K}=\mathrm{mgR}_{\mathrm{E}}\)
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