Question

A bullet weighing 10 g is fired with a velocity of 800 m/s. After passing through a mud wall 1 m thick, its velocity decreases to 100 m/s. Find the average resistance offered by the mud wall.

Answer 1

Answer:

a = (u^2 - v^2) / (2S)

= (800^2 - 100^2) / (2 × 1)

= 315000 m/s^2

F = ma

= 10 × 10^-3 × 315000

= 3150 N

Resistance offered by mud wall is 3150 N

Answer 2

GIVEN :-

A ʙᴜʟʟᴇᴛ ᴏғ ᴍᴀss 20g ɪs ғɪʀᴇᴅ ғʀᴏᴍ ᴀ ʀɪғʟᴇ ᴡɪᴛʜ ᴀ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ 800 m/s .

Aғᴛᴇʀ ᴘᴀssɪɴɢ ᴛʜʀᴏᴜɢʜ ᴀ ᴍᴜᴅ ᴡᴀʟʟ 100ᴄm ᴛʜɪᴄᴋ, ᴠᴇʟᴏᴄɪᴛʏ ᴅᴇᴏᴘs ᴛᴏ 100 m/s .

TO FIND :-

Tʜᴇ ᴀᴠᴇʀᴀɢᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴏғ ᴛʜᴇ ᴡᴀʟʟ .

SOLUTION :-

☯︎ ᴍᴀss ᴏғ ʙᴜʟʟᴇᴛ (m) = 20g = 0.02 kg

☯︎ Vᴇʟᴏᴄɪᴛʏ ᴏғ ʙᴜʟʟᴇᴛ ʙᴇғᴏʀᴇ ᴘᴀssɪɴɢ ᴛʜʀᴏᴜɢʜ ᴍᴜᴅ ᴡᴀʟʟ (ᴜ) = 800 m/s

☯︎ Vᴇʟᴏᴄɪᴛʏ ᴏғ ʙᴜʟʟᴇᴛ ᴀғᴛᴇʀ ᴘᴀssɪɴɢ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴍᴜᴅ ᴡᴀʟʟ (ᴠ) = 100 m/s

☯︎ Dɪsᴛᴀɴᴄᴇ ᴄᴏᴠᴇʀᴇᴅ ʙʏ ʙʏ ᴛʜᴇ ʙᴜʟʟᴇᴛ (s) = 100ᴄm = 1m

ʟᴇᴛ,

ᴀᴠᴇʀᴀɢᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴏғғᴇʀᴇᴅ ʙʏ ᴛʜᴇ ᴡᴀʟʟ = \bf\red{F}F

✯ Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴡᴏʀᴋ-ᴇɴᴇʀɢʏ ᴛʜᴇᴏʀᴇᴍ,

$\begin{gathered}\begin{cases} \text{Work done by} \\ \text{resistance offered} \\ \text{by mud wall} \end{cases}\Bigg\} = \begin{cases} \text{Decrease in} \\ \text{kinetic energy}\end{cases}\Bigg\}\end{gathered} ⎩⎪⎪⎨⎪⎪⎧$

$\huge\red\checkmark✓ \bf\purple{F\:.\:s\:=\:\dfrac{1}{2}\:m\:(u^2\:-\:v^2)\:}F.s=$

✯ Nᴏᴡ, ᴀᴠᴇʀᴀɢᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ɪs

$\bf\pink{:\implies\:F\:=\:\dfrac{m\:(u^2\:-\:v^2)}{2\:s}\:}:$

$\rm{:\implies\:F\:=\:\dfrac{0.02\:\times\:\Big\{(800)^2\:-\:(100)^2\Big\}}{2\:1}\:}:$

$\rm{:\implies\:F\:=\:\dfrac{0.02\times{(640000\:-\:10000)}}{2}\:}:$

$\rm{:\implies\:F\:=\:\dfrac{0.02\times{630000}}{2}\:}:$

$\rm{:\implies\:F\:=\:\dfrac{12600}{2}\:}$

$\bf\green{:\implies\:F\:=\:6300\:N\:}:$

$\huge\red\therefore$ [B] Tʜᴇ ᴀᴠᴇʀᴀɢᴇ ʀᴇsɪsᴛᴀɴᴄᴇ ᴏғ ᴛʜᴇ ᴡᴀʟʟ ɪs "6300 N" .