Consider two syringes with diameters of the smaller piston and larger piston being 1 cm and 3 cm respectively, excluding needle. Both are filled with water and are connected with a tightly fitted rubber tube filled with water. Now, if a force of 10 N is applied to the smaller piston, then what is the force exerted on the larger piston?

Question

Consider two syringes with diameters of the smaller piston and larger piston being 1 cm and 3 cm respectively, excluding needle. Both are filled with water and are connected with a tightly fitted rubber tube filled with water. Now, if a force of 10 N is applied to the smaller piston, then what is the force exerted on the larger piston? (A) 30 N (B) 60 N (C) 90 N (D) 100 N

Tardigrade Admin · Accepted Answer

Since pressure is transmitted undiminished throughout the water

∴ \frac{F _{1}}{A _{1}} = \frac{F _{2}}{A _{2}}

Where

F_{1}

and

F_{2}

are the forces on the smaller and on the larger pistons respectively and

A_{1}

and

A_{2}

are the respective areas.

∴ F_{2} = \frac{A _{2}}{A _{1}} F_{1} = \frac{π ( D _{2} /2 ) ^{2}}{π ( D _{1} /2 ) ^{2}} F_{1} = (\frac{D _{2}}{D _{1}})^{2} F_{1}

= \frac{( 3 \times ( 10 ) ^{- 2} m ) ^{2}}{( 1 \times ( 10 ) ^{- 2} m ) ^{2}} \times 10 N = 90 N

$30 N$

$60 N$

$90 N$

$100 N$

30N

60N

90N

100N

$30 N$

$60 N$

$90 N$

$100 N$