Q. A bullet moving with a speed of $100ms^{- 1}$ can just penetrate into two planks of equal thickness. Then if speed is doubled, what will be the number of such planks?
NTA AbhyasNTA Abhyas 2020
Solution:
Let retarding force is uniform and it is $F$
So,by work energy theorem $F\times 2S\times cos180^\circ =0-\frac{1}{2}\times m\times 100^{2}$
We get, $FS=2500\times m$ .......(i)
Now, let required plank are $n$ , So again by work energy theorem
$F\times nS\times cos180^\circ =0-\frac{1}{2}\times m\times \left(\right.200\left(\left.\right)^{2}$
By putting value from (i) $n\times \left(2500 \times m\right)=200\times 100\times m$
We get $n=8$
Let retarding force is uniform and it is $F$
So,by work energy theorem $F\times 2S\times cos180^\circ =0-\frac{1}{2}\times m\times 100^{2}$
We get, $FS=2500\times m$ .......(i)
Now, let required plank are $n$ , So again by work energy theorem
$F\times nS\times cos180^\circ =0-\frac{1}{2}\times m\times \left(\right.200\left(\left.\right)^{2}$
By putting value from (i) $n\times \left(2500 \times m\right)=200\times 100\times m$
We get $n=8$