Q123 / 160 · AP EAMCET 2019 (22 Apr Shift 1) · Physics

Assertion (A) The range of a projectile is maximum when the angle of projection is \(45^{\circ}\). Reason (R) The range of a projectile depends only on the angle of projection.

  • A
    Both (A) and (R) are true and (R) is the correct explanation of \((A)\).
  • B
    Both (A) and (R) are true but \((R)\) is not the correct explanation of \((A)\).
  • Correct answer
    C
    (A) is true but (R) is false.
  • D
    (A) is false but \((R)\) is true.

Solution

Assertion is true. (A) The range of projectile is maximum when the angle of projection is \(45^{\circ}\). \(R_{\max }=\frac{u^2 \sin (2 \times 45)}{g}=\frac{u^2}{g}\) But reason \((R)\) is false. \(\therefore\) Range of a projectile, \(R=\frac{u^2 \sin 2 \theta}{g}\) Hence, the range of projectile depends on the angle of projection \(\theta\) and initial velocity \(u\). \(\therefore\) (A) \(\rightarrow\) True (B) \(\rightarrow\) False

Hence, the correct answer is option: 'C'.

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