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 and 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. 60 N
C. 90 N
D. 100 N

Answer

C

Explanation

Since pressure is transmitted undiminished throughout the water
`therefore (F_(1))/(A_(1))=(F_(2))/(A_(2))`
where `F_(1)` and `F_(2)` are the forces on the smaller and one the larger pistons respectively and `A_(1) and A_(2)` are the respective areas.
`therefore F_(2) =(A_(2))/(A_(1))F_(1)=(pi(D_(2)//2)^(2))/(pi(D_(1)//D_(2))^(2))F_(1)=((D_(2))/(D_(1)))^(2)F_(1)`
`=((3xx10^(-2)m)^(2))/((1xx10^(-2)m)^(2))xx10N=90 N`