A bullet from a gun is fired on a rectangular wooden block with velocity <math> <mi>u</mi> </math> . When bullet travels <math> <mn>24</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> through the block along its length horizontally, velocity of bullet become <math> <mfrac> <mrow> <mrow> <mi>u</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> </math> . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

i series = E R series ⇒ i series = E 10 R i parallel = E R Parallel = E R / 10 i parallel = n × i series ⇒ 10 E R = n E 10 R ⇒ n = 100

A bullet from a gun is fired on a rectangular wooden block with velocity <math> <mi>u</mi> </math> . When bullet travels <math> <mn>24</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> through the block along its length horizontally, velocity of bullet become <math> <mfrac> <mrow> <mrow> <mi>u</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> </math> . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is: &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Physics NCERT Exemplar Solutions Class 11th Chapter Eight Physics Class 11th Work, Energy and Power

A bullet from a gun is fired on a rectangular wooden block with velocity $u$ . When bullet travels $24 c m$ through the block along its length horizontally, velocity of bullet become $\frac{u}{3}$ . Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

Option 1 -

$30 c m$

Option 2 -

$27 c m$

Option 3 -

$24 c m$

Option 4 -

$28 c m$

3 Views | Posted 4 weeks ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

4 weeks ago

Correct Option - 3

Detailed Solution:

$i_{series} = \frac{E}{R_{series}}$

$\Rightarrow i_{series} = \frac{E}{10 R}$

$i_{parallel} = \frac{E}{R_{Parallel}}$

$= \frac{E}{R / 10}$ $i_{parallel} = n \times i_{series}$

$\Rightarrow \frac{10 E}{R} = \frac{n E}{10 R}$

$\Rightarrow n = 100$

<math> <msub> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> <mrow> <mrow> <mtext>series</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>E</mi> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mtext>series</mtext> <mtext> </mtext> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> <math> <mo>⇒</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mrow> <mrow> <mtext>series</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow> <mrow> <mn>10</mn> <mi mathvariant="normal">R</mi> </mrow> </mrow> </mfrac> </math> <math> <msub> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mrow> <mrow> <mtext>parallel</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">R</mi> </mrow> </mrow> <mrow> <mrow> <mtext>Parallel</mtext> <mtext> </mtext> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">R</mi> <mo>/</mo> <mn>10</mn> </mrow> </mrow> </mfrac> </math> <math> <msub> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mrow> <mrow> <mtext>parallel</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>=</mo> <mi mathvariant="normal">n</mi> <mo>×</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </mrow> <mrow> <mrow> <mtext>series</mtext> <mtext> </mtext> </mrow> </mrow> </msub> </math> <math> <mo>⇒</mo> <mfrac> <mrow> <mrow> <mn>10</mn> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">R</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">E</mi> </mrow> </mrow> <mrow> <mrow> <mn>10</mn> <mi mathvariant="normal">R</mi> </mrow> </mrow> </mfrac> </math> <math> <mo>⇒</mo> <mi mathvariant="normal">n</mi> <mo>=</mo> <mn>100</mn> </math>

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