A body is allowed to fall from a height ‘h’ above the ground. Then match the following.
List – I List-II
(a) P.E. = K.E. (e) at height $\frac{h}{2}$
(b) P.E. = 2K.E (f) constant at any point
(c) K.E = 2P. E (g) at height of $\frac{2 h}{3}$
(d) P.E. + K.E (h) at height of $\frac{h}{3}$

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a-e, b-h, c-g, d-f

a-g b-e, c-f, d-h

a-f, b-g c-e d-h

a-e, b-g, c-h, d-f

answer is A.

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Detailed Solution

$(a) \Rightarrow P . E . = mg(height from the ground) K E = \frac{1}{2} m v^{2} w h e r e v^{2} = 2 g (d i s p l a c e m e n t f r o m t h e p o i n t w h e r e i t i s d r o p p e d) m i s m a s s; g i s a c c e l e r a t i o n d u e t o g r a v i t y; v i s v e l o c i t y * * * F o r a f r e e l y f a l l i n g b o d y w h e n i t f a l l s t h r o u g h a d i s \tan c e x f r o m a h e i g h t h i t s v l o c i t y i s g i v e n b y v = \sqrt{2 g x} a n d k . E = \frac{m v^{2}}{2} = m g x i t s h e i g h t f r o m t h e g r o u n d i s = h - x \frac{k . E}{p . E} = \frac{m g x}{m g (h - x)}$