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Physics
A girl in a swing is 2.5 m above ground at the maximum height and at 1.5 m above the ground at the lowest point. Her maximum velocity in the swing is (g = 10 ms-2)
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Q. A girl in a swing is $2.5\, m$ above ground at the maximum height and at $1.5 \,m$ above the ground at the lowest point. Her maximum velocity in the swing is ($g$ = $10\, ms^{-2}$)
KEAM
KEAM 2012
Work, Energy and Power
A
$5\sqrt{2 }ms^{-1}$
15%
B
$2\sqrt{5 }ms^{-1}$
58%
C
$2\sqrt{3 }ms^{-1}$
16%
D
$3\sqrt{2 }ms^{-1}$
8%
E
$4\sqrt{2 }ms^{-1}$
8%
Solution:
In this case,
Change in Potential energy = Kinetic energy
$\frac{1}{2} m v^{2} =m g\left(h_{2}-h_{1}\right) $
$v^{2} =2 g(2.5-1.5) $
$v^{2} =2 \times 10 \times 1$
$v =\sqrt{5 \times 2 \times 2} $
$v =2 \sqrt{5} m / s$