Two syringes of different cross-section (without needle filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston an larger piston are `1 cm` and `3 cm` respectively. If a force of 10N is applied to the smaller piston then the force exerted on the larger piston is

Options

A. 30N
B. 60N
C. 90N
D. 100N

Answer

C

Explanation

Since pressure is transmitted undiminished through out the water
`:. (F_1)/(A_1 = (F_2)/(A_2)`
Where ,`F_(1)` and `F_(2)` are the force on the smaller and on the larger pistons respectively and `A_(1)` and `A_(2)` are the respective areas.
`:. F_(2) = (A_2)/(A_1) F_(1) = (pi(D_(2)//2)^(2))/(pi(D_(1)//2)^(2))F_(1) = ((D_1)/(D_2))^(2)F_(1)`
`=((3xx10^(-2)m)^(2))/((1xx10^(-2)m)^(2)) xx 10 N =90N`.