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Physics NCERT Exemplar Solutions Class 11th Chapter Five Physics Class 12th Laws of Motion Physics NCERT Exemplar Solutions Class 12th Chapter Five

A body of mass M at rest explodes into pieces, in the ratio of masses 1 : 1: 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms^-¹ and 40 ms-¹ respectively. The velocity of the third piece will be:

Option 1 -

15 ms^-1

Option 2 -

25 ms^-1

Option 3 -

35 ms^-1

Option 4 -

50 ms^-1

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

Let ‘v’ be the velocity of third piece

com along x-axis

M × 0 = M₁v_x + M₃v’_x

$\Rightarrow 0 = M_{1} \times 30 + M_{3} v' x$

$v_{x} 1 = \frac{- M_{1}}{M_{3}} \times 30$

$\frac{- 1}{2} \times 30$

$v_{x}^{1} = - 15 m / s e c$

Com along y-a

...more

Let ‘v’ be the velocity of third piece

com along x-axis

M × 0 = M₁v_x + M₃v’_x

$\Rightarrow 0 = M_{1} \times 30 + M_{3} v' x$

$v_{x} 1 = \frac{- M_{1}}{M_{3}} \times 30$

$\frac{- 1}{2} \times 30$

$v_{x}^{1} = - 15 m / s e c$

Com along y-axis

M × 0 = M₂v_y + M₃v’_y

v_y = $\frac{- M_{2}}{M_{3}} v_{y}$

v_y = $\frac{- 1}{2} \times 40$

v_y = -20m/sec

^{$\vec{v} = - 15 \hat{i} - 20 \hat{j}$}

v = $\sqrt[]{1 5^{2} + 2 0^{2}} = \sqrt[]{225 + 400} = 25 m / s e c$

less

Let ‘v’ be the velocity of third piece                                    com along x-axis              M × 0 = M1vx + M3v’x      <math> <mrow> <mo>⇒</mo> <mn>0</mn> <mo>=</mo> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>×</mo> <mn>3</mn> <mn>0</mn> <mo>+</mo> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mi>v</mi> <mo>'</mo> <mi>x</mi> </mrow> </math>                 <math> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mn>1</mn> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> <mo>×</mo> <mn>3</mn> <mn>0</mn> </mrow> </math> <math> <mrow> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>×</mo> <mn>3</mn> <mn>0</mn> </mrow> </math> <math> <mrow> <msubsup> <mrow> <mi>v</mi> </mrow> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mn>5</mn> <mi>m</mi> <mo>/</mo> <mi>s</mi> <mi>e</mi> <mi>c</mi> </mrow> </math>                           Com along y-axis              M × 0 = M2vy + M3v’y              vy =   <math> <mrow> <mfrac> <mrow> <mo>−</mo> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>M</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>y</mi> </mrow> </msub> </mrow> </math>               vy =   <math> <mrow> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>×</mo> <mn>4</mn> <mn>0</mn> </mrow> </math>               vy = -20m/sec <math> <mrow> <mover accent="true"> <mi>v</mi> <mo>→</mo> </mover> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mn>5</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>−</mo> <mn>2</mn> <mn>0</mn> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> </mrow> </math>                v =   <math> <mrow> <mroot> <mrow> <mn>1</mn> <msup> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mn>2</mn> <mn>2</mn> <mn>5</mn> <mo>+</mo> <mn>4</mn> <mn>0</mn> <mn>0</mn> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mn>2</mn> <mn>5</mn> <mi>m</mi> <mo>/</mo> <mi>s</mi> <mi>e</mi> <mi>c</mi> </mrow> </math>

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A body of mass M at rest explodes into pieces, in the ratio of masses 1 : 1: 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms^-¹ and 40 ms-¹ respectively. The velocity of the third piece will be:

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A body of mass M at rest explodes into pieces, in the ratio of masses 1 : 1: 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms-1 and 40 ms-1 respectively. The velocity of the third piece will be:

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A body of mass M at rest explodes into pieces, in the ratio of masses 1 : 1: 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms^-¹ and 40 ms-¹ respectively. The velocity of the third piece will be: