Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If a body is projected from the earth's surface with a speed of 3v_e (where v_e is the escape velocity), its speed at interstellar distance (infinity) is 2 2 v_e . Reason (R): For a body projected with a speed v > v_e , its speed at infinity is not given by the linear difference (v - v_e) . In the

Step-by-step solution

Assertion (A) is true: By the conservation of mechanical energy, the velocity of a body at infinity ( v_ ) when projected with a velocity v is given by v_ = v^2 - v_e^2 . Substituting v = 3v_e : v_ = (3v_e)^2 - v_e^2 = 9v_e^2 - v_e^2 = 8v_e^2 = 2 2 v_e . Reason (R) is true: The speed at infinity is indeed not calculated by the linear subtraction v - v_e . A common misconception is to write v_ = 3v_e - v_e = 2v_e , which is incorrect. However, Reason (R) is merely a negative statement pointing out that the linear fo