A shell of mass <math> <mi>m</mi> </math> is at rest initially. It explodes into three fragments having mass in the ratio <math> <mn>2</mn> <mo>:</mo> <mn>2</mn> <mo>:</mo> <mn>1</mn> </math> . If the fragments having equal mass fly off along mutually perpendicular directions with speed <math> <mi>v</mi> </math> , the speed of the third (lighter) fragment is :

By conservation of momentum: m ( 0 ) = 2 m 5 ( - v i ˆ ) + 2 m 5 ( - v j ˆ ) + m 5 v ? ' ⇒ v ? ' = 2 v i ˆ + 2 v j ˆ ⇒ v ' = ( 2 v ) 2 + ( 2 v ) 2 = 2 2 v

A shell of mass <math> <mi>m</mi> </math> is at rest initially. It explodes into three fragments having mass in the ratio <math> <mn>2</mn> <mo>:</mo> <mn>2</mn> <mo>:</mo> <mn>1</mn> </math> . If the fragments having equal mass fly off along mutually perpendicular directions with speed <math> <mi>v</mi> </math> , the speed of the third (lighter) fragment is : &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

Ask & Answer Question

System of Particles and Rotational Motion physics ncert solutions class 11th Physics Class 11th

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2 : 2 : 1$ . If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$ , the speed of the third (lighter) fragment is :

Option 1 -

$v$

Option 2 -

$\sqrt[]{2} v$

Option 3 -

$2 \sqrt[]{2} v$

Option 4 -

$3 \sqrt[]{2} v$

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 3

Detailed Solution:

<div class="photo-widget-full"><div class="figure"><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1756969596phpJCO8cT.jpeg" alt="" width="252" height="94" loading="lazy"></picture></div></div>By conservation of momentum: <math> <mtable columnalign="right"> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi>m</mi> <mo> (</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> <mo> (</mo> <mo>-</mo> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> <mo> (</mo> <mo>-</mo> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <mrow> <mi>m</mi> </mrow> </mrow> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> </mfrac> <msup> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">'</mi> </mrow> </mrow> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>⇒</mo> <msup> <mrow> <mrow> <mover accent="true"> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mo>? </mo> </mover> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">'</mi> </mrow> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> <mo>+</mo> <mn>2</mn> <mi>v</mi> <mover accent="true"> <mrow> <mrow> <mi>j</mi> </mrow> </mrow> <mi>ˆ</mi> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>⇒</mo> <msup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">'</mi> </mrow> </mrow> </msup> <mo>=</mo> <mroot> <mrow> <mrow> <mo> (</mo> <mn>2</mn> <mi>v</mi> <msup> <mrow> <mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>+</mo> <mo> (</mo> <mn>2</mn> <mi>v</mi> <msup> <mrow> <mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi> </mi> <mo>=</mo> <mn>2</mn> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mi>v</mi> </mrow> </mtd> </mtr> </mtable> </math> </div></div>

0 Upvotes 0 Downvotes

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2 : 2 : 1$ . If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$ , the speed of the third (lighter) fragment is :

1 Answer

Similar Questions for you

Learn more about...

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

A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1 . If the fragments having equal mass fly off along mutually perpendicular directions with speed v , the speed of the third (lighter) fragment is :

1 Answer

Similar Questions for you

Learn more about...

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

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2 : 2 : 1$ . If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$ , the speed of the third (lighter) fragment is :