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Most Important Selected Qs for JEE AdvancedPhysicsGravitation

Two particles are projected vertically upwards from the surface of the earth with velocities v 1 = 2 g R 3 and v 2 = 4 g R 3 respectively. If the maximum heights attained by the two particles are h 1 and h 2 respectively, then calculate the ratio h 1 h 2 .

Correct answer

.25

Step-by-step solution

Loss of KE = Gain in PE ⇒ 1 2 mv 2 = mgh R h + R CASE I. ⇒ 1 2 m 2 gR 3 = mgh 1 R h 1 + R ...(i) ⇒ 1 2 m 4 g R 3 = mgh 2 R h 2 + R ...(ii) Solving (i) ⇒ 1 3 = h 1 h 1 + R ⇒ h 1 = R 2 ...(iii) Solving (ii) ⇒ 2 3 = h 2 h 2 + R ...(iv) ⇒ h 2 = 2 R From (iii) and (iv) ⇒ h 1 h 2 = R / 2 2 R ∴ h 1 h 2 = 1 4 = 0 . 25

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