A stone of mass 10 g is thrown vertically upwards. Its minimum and maximum distance from a fixed point A is 6 m and 6√5 m, respectively. When the stone is at the maximum height, it is at a distance 10 m from point A. find initial kinetic energy of the ball.

Q: A stone of mass 10 g is thrown vertically upwards. Its minimum and maximum distance from a fixed point A is 6 m and 6√5 m, respectively. When the stone is at the maximum height, it is at a distance 10 m from point A. find initial kinetic energy of the ball.

(a) 1 J

(b) 2 J

(c) 3 J

(d) 4 J

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Ans: (b)

Sol: Numerical

$\displaystyle QO = \sqrt{(6\sqrt{5})^2 – 6^2}$

QO = 12 m

$\displaystyle OP = \sqrt{10^2 – 6^2}$

OP = 8 m

Maximum height attained by stone is

H = QO + OP = 12 + 8 = 20 m

By using formula ,

$\displaystyle v^2 = u^2 – 2 g H $

$\displaystyle 0 = u^2 – 2 \times 10 \times 20 $

$\displaystyle u^2 = 400 $

u = 20 m/s

Initial Kinetic Energy will be

$\displaystyle K.E = \frac{1}{2} m u^2 $

$\displaystyle K.E = \frac{1}{2} \times 10 \times 10^{-3} \times 20^2 $

K.E = 2 J