Question

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Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A piston of cross section area =100cm²
• Exert a force of =10⁷dyne
• Having Other piston supports having mass of 2000kg

${\sf{\green{\underline{\large{To\:find}}}}}$

• Cross section area of other piston

${\sf{\pink{\underline{\Large{Explanation}}}}}$

we know that

$\boxed{\boxed{\sf\red{Pressure=\dfrac{Force}{Area}}}}$

Changing the units

Piston 1

• Area =100cm²a=0.01M²

• Force=10⁷dyne=10³N

Here pressure

$\boxed{\boxed{\sf\red{Pressure=\dfrac{Force}{Area}}}}$

$\implies\tt\dfrac{100}{0.01}$

$\implies\tt{100\times{100}}$

=>10000

Piston 2

• From Pascal law The pressure on fluids are eual

Therefore

• Piston1=Piston2=Pressure

Force = m×a(gravity)

=>f=2000kg×10m/s²

=>20000N

Now

$\boxed{\boxed{\sf\red{Pressure=\dfrac{Force}{Area}}}}$

Putting values

$\implies\tt{10000}=\dfrac{20000}{Area}$

Area=2m²

changing into cm²

=>2×100×100

=>2×10⁴

Answer 2

$\large{\red{ \bf{ \underline {\underline{Answer}}}}} \\ \\ \purple{ \sf{\mapsto 2 \times {10}^{4} \: {cm}^{2} }} \\ \\ \mathbf{\green{ \underline{Given}}} \\ \\ \sf{ \rightsquigarrow Piston \: of \: cross \: section \: area = 100 \: {m}^{2} } \\ \\ \sf{ \rightsquigarrow Exert \: a \: force = {10}^{7} } \\ \\ \sf{ \rightsquigarrow Other \: piston \: supports \: having \: mass = 200 \: Kg}\\ \\ \mathbf {\blue{ \underline{ To \: Find}}} \\ \\ \sf{ \rightsquigarrow Cross \: section \: area \: of \: other \: position\:=\:?}$

⠀⠀

❏ According To Given Question

⠀⠀

$\text {\sf{By Pascal's law of transmission of fluid pressure.}} \\ \text{\sf{The pressure from piston 1 is equally transmitted}} \\ \sf{ to \: piston \: 2.} \\ \\ \sf{ \implies P_1=P_2}\\ \\ \sf{ \implies \frac{F_1}{A_1}= \frac{F_2}{P_2}}\\ \\ \sf{ \implies F_1 = {10}^{7} \: dyne} \\ \\ \sf{ \implies F_1= {10}^{2} \: N } \\ \\ \sf{ \implies A_1 = \: 100 \: {cm}^{2} = \frac{100}{1000 } } \\ \\ \sf{ \implies A_1 = {10}^{ - 2} \: {m}^{2} } \\ \\ \sf{ \implies F_2 = Mg = 2000 \: Kg \times 10 \: m/s} \\ \\ \sf{ \implies F_2 = 20000 \: N} \\ \\ \sf{ \implies A_2 = \: ?} \\ \\ \sf{ \implies \frac{ {10}^{2} }{ {10}^{ - 2} } } = \frac{20000}{A_2} \\ \\ \sf{ \implies {10}^{4} \: A_2 = 20000} \\ \\ \sf{ \implies A_2 = \frac{2 \cancel{0000}}{1 \cancel{0000} }} \\ \\ \sf{ \implies A_2 = 2 \: {m}^{2} } \\ \\ \sf{ A_2 \: must \: be \: 2 \: {m}^{2} } \\ \\ \sf{ \purple{ \implies}} \purple{ \underline{ \boxed{ \sf{2 \times {10}^{4} \: {cm}^{2} }}}} \\ \\ \rm{\therefore\:\:Option\:(C)\:is \:right\:\checkmark}$