In a rocket, fuel burns at the rate of 1 $k g / s .$ This fuel is ejected from the rocket with a velocity of 60 $k m / s$ . This exerts a force on the rocket equal to

Option 1 -

6000 N

Option 2 -

60000N

Option 3 -

60N

Option 4 -

600N

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Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 2

Detailed Solution:

Rate of burning of fuel $(\frac{d m}{d t}) = 1 k g / s$ and velocity of ejected fuel

$(v) = 60 k m / s$

$= 60 \times 1 0^{3} m / s .$

Forcev = Rate of change of momentum

$= \frac{d p}{d t} = \frac{d (m ν)}{d t} = v \frac{d m}{d t} = (60 \times 1 0^{3}) \times 1$

$= 60000$ N.

Rate of burning of fuel <math> <mrow> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <mi>d</mi> <mi>m</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mi>k</mi> <mi>g</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1819704535"> </o:OLEObject></xml><! [endif]-> and velocity of ejected fuel <math> <mrow> <mrow> <mo> (</mo> <mrow> <mi>v</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>6</mn> <mn>0</mn> <mi>k</mi> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math> <math> <mrow> <mo>=</mo> <mn>6</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> <mi>m</mi> <mo>/</mo> <mi>s</mi> <mo>.</mo> </mrow> </math>  <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1819704536"> </o:OLEObject></xml><! [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1819704537"> </o:OLEObject></xml><! [endif]->Forcev = <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1819704538"> </o:OLEObject></xml><! [endif]-> Rate of change of momentum <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mi>p</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mrow> <mo> (</mo> <mrow> <mi>m</mi> <mi>ν</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mi>v</mi> <mfrac> <mrow> <mi>d</mi> <mi>m</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mrow> <mo> (</mo> <mrow> <mn>6</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>×</mo> <mn>1</mn> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1819704539"> </o:OLEObject></xml><! [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1030" DrawAspect="Content" ObjectID="_1819704540"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mo>=</mo> <mn>6</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> <mn>0</mn> </mrow> </math> N.

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In a rocket, fuel burns at the rate of 1 $k g / s .$ This fuel is ejected from the rocket with a velocity of 60 $k m / s$ . This exerts a force on the rocket equal to

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In a rocket, fuel burns at the rate of 1 k g / s . This fuel is ejected from the rocket with a velocity of 60 k m / s . This exerts a force on the rocket equal to

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In a rocket, fuel burns at the rate of 1 $k g / s .$ This fuel is ejected from the rocket with a velocity of 60 $k m / s$ . This exerts a force on the rocket equal to