A body <math> <mi>A</mi> </math> <math></math> , of mass <math> <mi>m</mi> <mo>=</mo> <mn>0.1</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </math> <math><mtext></mtext></math> has an initial velocity of <math> <mn>3</mn> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> <msup> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> <math><mover accent="true"><mrow><mrow></mrow></mrow></mover><msup><mrow><mrow><mtext></mtext></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> . It collides elastically with another body, <math> <mi>B</mi> </math> <math></math> of the same mass which has an initial velocity of <math> <mn>5</mn> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> <msup> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> <math><mover accent="true"><mrow><mrow></mrow></mrow></mover><msup><mrow><mrow><mtext></mtext></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> . After collision, A moves with a velocity <math> <mover accent="true"> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mo>?</mo> </mover> <mo>=</mo> <mn>4</mn> <mo>(</mo> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> <mo>+</mo> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>&circ;</mi> </mover> <mo>)</mo> </math> <math><mover accent="true"><mrow><mrow></mrow></mrow></mover><mover accent="true"><mrow><mrow></mrow></mrow></mover><mover accent="true"><mrow><mrow></mrow></mrow></mover></math> . The energy of <math></math> <math> <mi>B</mi> </math> after collision is written as <math><mfrac><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></mfrac><mtext></mtext></math> <math> <mfrac> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> </mfrac> <mtext> </mtext> <mi mathvariant="normal">J</mi> </math> . The value of <math> <mi>x</mi> </math> <math></math> is

For elastic collision K E i = K E r 1 2 m × 25 + 1 2 × m × 9 = 1 2 m × 32 + 1 2 m v 2 34 = 32 + v 2 K E = 1 2 × 0.1 × 2 = 0.1 J = 1 10 x = 1

Ask & Answer Question

Physics NCERT Exemplar Solutions Class 12th Chapter Fifteen Kinetic Energy Work, Energy and Power Physics Class 11th

A body $A$ , of mass $m = 0.1 k g$ has an initial velocity of $3 \hat{i} {m s}^{- 1}$ $^{}$ . It collides elastically with another body, $B$ of the same mass which has an initial velocity of $5 \hat{j} {m s}^{- 1}$ $^{}$ . After collision, A moves with a velocity $\overset{?}{v} = 4 (\hat{i} + \hat{j})$ . The energy of $B$ after collision is written as $\frac{}{}$ $\frac{x}{10} J$ . The value of $x$ is

3 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

For elastic collision ${K E}_{i} = {K E}_{r}$

$\frac{1}{2} m \times 25 + \frac{1}{2} \times m \times 9 = \frac{1}{2} m \times 32 + \frac{1}{2} m v^{2}$

$34 = 32 + v^{2}$

$K E = \frac{1}{2} \times 0.1 \times 2 = 0.1 J = \frac{1}{10}$

$x = 1$

For elastic collision   <math> <msub> <mrow> <mrow> <mi mathvariant="normal">K</mi> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">K</mi> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> </math> <math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>25</mn> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo>×</mo> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>9</mn> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>32</mn> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>m</mi> <msup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> <math> <mn>34</mn> <mo>=</mo> <mn>32</mn> <mo>+</mo> <msup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> <math> <mi mathvariant="normal">K</mi> <mi mathvariant="normal">E</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo>×</mo> <mn>0.1</mn> <mo>×</mo> <mn>2</mn> <mo>=</mo> <mn>0.1</mn> <mtext> </mtext> <mi mathvariant="normal">J</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> </mfrac> </math> <math> <mi>x</mi> <mo>=</mo> <mn>1</mn> </math>

0 Upvotes 0 Downvotes

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question