Physics · Acceleration due to gravity and its variation with altitude and depth
Assertion A particle is projected upwards with speed and it goes to a height If
Assertion A particle is projected upwards with speed \( v \) and it goes to a height \( h . \) If we double the speed then it will move to height \( 4 h \) Reason In case of earth, acceleration due to gravity \( g \) varies as \( g \propto \frac{1}{r^{2}} r \geq R \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Both Assertion and Reason are incorrect
Step-by-step solution
The assertion is correct under the assumption of constant gravitational acceleration (g), which yields h ∝ v². However, the reason correctly states that Earth's gravity varies inversely with the square of distance from the center. This variation does not support the assertion's proportionality; in fact, for large heights, the exact relationship deviates from h ∝ v². Thus, both statements are individually correct, but the reason does not explain the assertion.
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