JEE MAIN - Physics (2021 - 31st August Morning Shift - No. 24)
A block moving horizontally on a smooth surface with a speed of 40 ms$$-$$1 splits into two equal parts. If one of the parts moves at 60 ms$$-$$1 in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = ___________.
Answer
1
Explanation
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Pi = Pf
m $$\times$$ 40 = $${m \over 2}$$ $$\times$$ v + $${m \over 2}$$ $$\times$$ 60
40 = $${v \over 2}$$ + 30
$$\Rightarrow$$ v = 20
(K. E.)I = $${1 \over 2}$$m $$\times$$ (40)2 = 800 m
(K. E.)f = $${1 \over 2}$$$${m \over 2}$$ . (20)2 + $${1 \over 2}$$ . $${m \over 2}$$ (60)2 = 1000 m
| $$\Delta$$ K. E. | = | 1000m $$-$$ 800 m | = 200 m
$${{\Delta K.E.} \over {{{(K.E.)}_i}}} = {{200m} \over {800m}} = {1 \over 4} = {x \over 4}$$
x = 1
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