Assertion: The escape speed does not depend o | vedclass

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(B) The escape speed from the surface of the Earth is given by the formula $v_e = \sqrt{\frac{2GM}{R}}$. This formula depends only on the gravitationa

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If both $Assertion$ and $Reason$ are correct but $Reason$ is not a correct explanation of the $Assertion$.

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(B) The escape speed from the surface of the Earth is given by the formula $v_e = \sqrt{\frac{2GM}{R}}$. This formula depends only on the gravitational constant $G$,the mass of the Earth $M$,and the radius of the Earth $R$. It does not depend on the direction of projection. Thus,the $Assertion$ is correct. The $Reason$ states that it is easier to attain escape speed if fired in the direction of Earth's rotation. This is true because the rotation of the Earth provides an initial tangential velocity to the projectile. However,this initial velocity effectively reduces the amount of additional velocity required to reach the escape speed relative to the Earth's surface,but it does not change the value of the escape speed itself. Therefore,the $Reason$ is a correct statement,but it does not explain why the escape speed (a fixed physical constant for a given planet) is independent of direction. Thus,the $Reason$ is not the correct explanation of the $Assertion$.

$Assertion$: The escape speed does not depend on the direction in which the projectile is fired.
$Reason$: Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the Earth rotates about its axis.

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$Assertion$: The escape speed does not depend on the direction in which the projectile is fired. $Reason$: Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the Earth rotates about its axis.