A block moving horizontally on a smooth surface with a speed of 40 m/s splits into parts with masses in the ratio of 1:2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is:-

Option 1 - <math> <mrow> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

Option 2 - <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> </math>

Option 3 - <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> </math>

Option 4 - <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>8</mn> </mrow> </mfrac> </mrow> </math>

3 Views|Posted 8 months ago

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Vishal Baghel | Contributor-Level 10

8 months ago

Correct Option - 4

Detailed Solution:

Using conservation of linear momentum:

=> 40 * 3m = 60 * m + v * 2m

=> v = 30 m/s

$K E_{i} = \frac{1}{2} * 3 m * {(40)}^{2}$

$K E_{f} = \frac{1}{2} * m * {(60)}^{2} + \frac{1}{2} * 2 m * {(30)}^{2}$

$\Rightarrow \frac{K E_{f}}{K E_{i}} = \frac{54}{48}$

Fractional change in kinetic energy = 1 $- \frac{K E_{f}}{K E_{i}} = \frac{1}{8}$

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Physics Work, Energy and Power 2021

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