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A boy drops a ball of $100 g$ from a height of $10 m$ . Then its kinetic energy at the height of $4 m$ above the surface of the earth and its total mechanical energy will be__

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6 J; 10 J

4 J; 6 J

4.2 J; 4 J

5 J; 10 J

answer is A.

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Detailed Solution

A boy drops a ball of

100 g

from a height of

10 m

. Then its kinetic energy at the height of

4 m

above the surface of the earth will be

6 J

, and its total mechanical energy will be

10 J

.
Given,

mass = 100 g

= 0.1 kg

height = 10 m

To find:
KE at the height of

4 m

above the surface.
K.E. at height

4 m

= \frac{1}{2} m v^{2}

……….eq.1
When a ball reaches

4 m

above the ground, it has travelled = (

10 - 4) m

= 6 m

distance.
Then the velocity of the ball at this height will be__

v^{2} = u^{2} + 2 as

(a = g = 10 m / s^{2} .)

v^{2} = 0 + 2 \times 10 \times 6

v = 2 \sqrt 30

……..eq. 2
Put the value of velocity from eq. 2 into eq. 1.

K . E . = \frac{1}{2} \times 0.1 \times 4 \times 30

= 6 J .

10 m

height,

mechanical energy = potential energy + Kinetic energy

\Rightarrow

= mgh + 0 (since the KE at the max . height is zero)

\Rightarrow

= 0.1 \times 10 \times 10

\Rightarrow

= 10 J

4 m

height, mechanical energy

= K . E . + P . E

\Rightarrow

= 6 J + 0.1 \times 10 \times 4

\Rightarrow

= 10 J

Hence, the mechanical energy remains the same or constant.

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