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Work, Energy, and Power physics ncert solutions class 11th Physics Class 11th Physics NCERT Exemplar Solutions Class 11th Chapter Six

Two identical steel cubes (masses 50g, side 1cm) collide head-on face to face with a speed of 10cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y= 2 × 10¹¹ N/m².

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Payal Gupta | Contributor-Level 10

3 months ago

This is a long answer type question as classified in NCERT Exemplar

m =50g = 50 $\times 10^{3} k g$

Side = 1cm = 0.01m

Speed v = 0.1m/s

Young’s modulus= 2 $\times 10^{11} N / m$ ²

According to the formula

F/A= Y $\frac{? L}{L}$

And F= K $? L$ where K is the compression in the spring.

K= YA/L = YL

Initial KE= 2 (1/2mv²)= 5 $\times 10^{- 4} J$

Final PE= 2 (1/2)K ( $? L$ )²

$? L = \sqrt[]{\frac{K E}{E}} = \sqrt[]{\frac{K E}{Y L}}$ = $\sqrt[]{\frac{5 \times 10^{- 4}}{2 \times 10^{11} \times 0.1}} = 1.58 \times 10^{- 7} m$

This is a long answer type question as classified in NCERT Exemplarm =50g = 50 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> <mi>k</mi> <mi>g</mi> </math> Side = 1cm = 0.01mSpeed v = 0.1m/sYoung’s modulus= 2 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>11</mn> </mrow> </mrow> </msup> <mi>N</mi> <mo>/</mo> <mi>m</mi> </math> 2According to the formulaF/A= Y <math> <mfrac> <mrow> <mrow> <mo>? </mo> <mi>L</mi> </mrow> </mrow> <mrow> <mrow> <mi>L</mi> </mrow> </mrow> </mfrac> </math> And F= K <math> <mo>? </mo> <mi>L</mi> </math>  where K is the compression in the spring.K= YA/L = YLInitial KE= 2 (1/2mv2)= 5 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> <mi>J</mi> </math> Final PE= 2 (1/2)K ( <math> <mo>? </mo> <mi>L</mi> </math> )2 <math> <mo>? </mo> <mi>L</mi> <mo>=</mo> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>K</mi> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mrow> <mi> </mi> <mfrac> <mrow> <mrow> <mi>K</mi> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <mi>Y</mi> <mi>L</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> </math>  = <math> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>5</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>11</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>0.1</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mn>1.58</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </mrow> </msup> <mi>m</mi> </math>

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(c) When M1 comes in contact with the spring. M1 is retarded by the spring force and M2 is accelerated by the spring force.

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(b) conserving energy between “O” ans ”A”

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(v’)²=v²-2gh = v^’= $\sqrt[]{v^{2} - 2 g h}$ ……….1

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1/2m(v₁)²=1/4m(v’)²=1/4m[v²-2gh]

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This is a multiple choice answer as classified in NCERT Exemplar

(b) conserving energy between “O” ans ”A”

U_i+ K_i= U_f+ K_f

0+1/2mv²= mgh + 1/2mv’

$\frac{{(v')}^{2}}{2} = \frac{v^{2}}{2} = - g h$

(v’)²=v²-2gh = v^’= $\sqrt[]{v^{2} - 2 g h}$ ……….1

Let speed after emerging be v₁then

=1/2mv₁²=1/2[1/2mv’²]

1/2m(v₁)²=1/4m(v’)²=1/4m[v²-2gh]

V₁= $\sqrt[]{\frac{v^{2}}{2} - g h}$ ………….2

From eqn 1 and 2

$\frac{v'}{v_{1}} = \frac{\sqrt[]{v^{2} - 2 g h}}{\sqrt[]{v^{2} - 2 g h / \sqrt[]{2}}} = \sqrt[]{2}$

So v₁ = v’/ $\sqrt[]{2}$ =v²(v’/2)

v₁>v’/2

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This is a multiple choice answer as classified in NCERT Exemplar

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Two identical steel cubes (masses 50g, side 1cm) collide head-on face to face with a speed of 10cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y= 2 × 10¹¹ N/m².

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Two identical steel cubes (masses 50g, side 1cm) collide head-on face to face with a speed of 10cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y= 2 × 1011 N/m2.

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Two identical steel cubes (masses 50g, side 1cm) collide head-on face to face with a speed of 10cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y= 2 × 10¹¹ N/m².