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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Motion in One Dimension

NTA Abhyas 2020 · Physics · Motion in One Dimension

A balloon rises from rest with a constant acceleration of (g)/(8) ....

A balloon rises from rest with a constant acceleration of g8\dfrac{g}{8}. A stone is released from it when it has risen to height hh. The time taken by the stone to reach the ground is nhgn\sqrt{\dfrac{h}{g}} seconds. Then what is the value of nn?

Correct answer

2

Step-by-step solution

From equation v2=u2+2as{v}^{2} = {u}^{2} + 2as

Given, u=0,a=g8u = 0, a = \dfrac{g}{8}

∴∴ We have, v=2(g8)hv = \sqrt{2\left(\dfrac{g}{8}\right)h}

When the stone released from this balloon. It will go upward with velocity v=ghv = \sqrt{gh}

In this condition, time taken by stone to reach the ground,

−h=vt−12gt2- h = vt - \dfrac{1}{2} g{t}^{2}

t=vg[1+1+2ghv2]t = \dfrac{v}{g}\left[1 + \sqrt{1 + \dfrac{2gh}{{v}^{2}}}\right]

=gh2g[1+1+2ghgh4]= \dfrac{\dfrac{\sqrt{gh}}{2}}{g}\left[1 + \sqrt{1 + \dfrac{2gh}{\dfrac{gh}{4}}}\right]

=2ghg=2hg= \dfrac{2\sqrt{gh}}{g} = 2\sqrt{\dfrac{h}{g}}
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