A 500g ball is released from a height of 4m . Each time it makes...

A $500g$ ball is released from a height of $4m$ . Each time it makes contact with the ground, it loses $25%$ of its kinetic energy. Find the kinetic energy it possess just after the ${3}^{rd}$ hit

Options

A $15J$
B $11.25J$
C $8.44J$
Dnone of these

Correct answer

C. $8.44J$

Step-by-step solution

After first hit

K . {E}_{1} = e^{2}K . E

3 / 4K . E = e^{2}K . E ⇒ e^{2} = 3 / 4

K . E . afterthirdhit ={( e^{2} )}^{3}

KE = \dfrac{27}{64} mgh= \dfrac{27}{64}

\left(\dfrac{1}{2} .10.4\right)

<br /><br />

= 27\left(

\dfrac{5}{16}\right) = \dfrac{135}{16} =

8.44J

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