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Grade 11Mechanics

A bullet on penetrating 2 successive wooden planks of unqual thickness loses its velocity by 200meter per second in each case. If the initial velocity is 1000meter per second calculate the ratio of thickness of the Planks.

Esha Bhattacharya

8 Years agoGrade 11

2 Answers

Eshan

8 Years ago

Loss in kinetic energy of bulletthrough a block $\propto$ thickness of the block.

Hence for the first block

$\dfrac{1}{2}m(1000^2-200^2)\propto t_1$

for the second block,

$\dfrac{1}{2}m(200^2-0^2)\propto t_2$

$\implies \dfrac{t_1}{t_2}=\dfrac{1000^2-200^2}{200^2}=24$

Ankan Pal

6 Years ago

Initial velocity-1000 m/S

After penetrating 1st block final velocity -(1000-200)=800 m/S

For 2nd block initial velocity-800m/S

Final velocity-600 m/S

Now,

V1^2=u1^2-2as1

2as1=u^2-v^2. _(1)

as1=18000

V2^2=u2^2-2as2

2as2=u2^2-v2^2

as2=14000. _(2)

Now (1)÷(2)= as1÷as2=18000÷14000

S1:s2= 9:7

Hence the ratio of the thickness of the planks are 9:7

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