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NEET 2021
Exam
NEET
Year
2021
Subject
Physics
Chapter
Gravitation

NEET 2021 · Physics · Gravitation

A particle of mass m is projected with a velocity v = k V _ e ( k <...

A particle of mass mm is projected with a velocity v=kVe(k<1)v = k{V}_{e} ( k < 1 ) from the surface of the earth (Ve={V}_{e} = escape velocity). The maximum height above the surface reached by the particle is___A particle of mass m is projected with a velocity v = k V _ e ( k < 1 ) from the surface of the earth ( V _ e = escape

Options

  1. AR{\left(\dfrac{k}{1 - k}\right)}^{2}
  2. BR{\left(\dfrac{k}{1 + k}\right)}^{2}
  3. CRk21−k2\dfrac{R{k}^{2}}{1 - {k}^{2}}
  4. DR2k1+k\dfrac{{R}^{2}k}{1 + k}

Correct answer

C. Rk21−k2\dfrac{R{k}^{2}}{1 - {k}^{2}}

Step-by-step solution

v = k{V}_{e} ( k < 1 )</p><p><imgsrc="https://cdn−question−pool.getmarks.app/pyq/neet/4cda8681−3cac−4e7c−a2d8−0a8cab3ee319−image.png"style="width:180px;height:232px;"/></p><p></p><p><img src="https://cdn-question-pool.Quantrex.app/pyq/neet/4cda8681-3cac-4e7c-a2d8-0a8cab3ee319-image.png" style="width: 180px; height: 232px;" /></p><p>\dfrac{1}{2}m{v}^{2} - \dfrac{GMm}{R} = 0 - \dfrac{GMm}{R + h}</p><p></p><p>\dfrac{1}{2}m{k}^{2} \times \dfrac{2GM}{R} - \dfrac{GMm}{R} = - \dfrac{GMm}{R + h}(∵Ve=2GMR)\left(∵ {V}_{e} = \sqrt{\dfrac{2GM}{R}}\right)

GMmk2R=−GMm(1R+h−1R)GMm\dfrac{{k}^{2}}{R} = - GMm\left(\dfrac{1}{R + h} - \dfrac{1}{R}\right)

k2R=hR(R+h)⇒1+Rh=1k2\dfrac{{k}^{2}}{R} = \dfrac{h}{R ( R + h )} ⇒ 1 + \dfrac{R}{h} = \dfrac{1}{{k}^{2}}

⇒Rh=1k2−1⇒ \dfrac{R}{h} = \dfrac{1}{{k}^{2}} - 1

⇒h=RK21−k2⇒ h = \dfrac{R{K}^{2}}{1 - {k}^{2}}

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