GATE Chemical 2019 | Question: 23

Question

For a hydraulic lift with dimensions shown in figure, assuming $g=10\:m/s^{2}$, the maximum diameter  $D_{left}$ (in $m$) that lifts a vehicle of mass $1000 \:kg$ using a force of $100 \:N$ is ____________________ (rounded off to two decimal places).

Answer 1

Use P=F/A

As P is equal at both point as these points are connected by same liquid and at same hight

so P1 = P2

so

F1/A1  = F2/A2

so F1= 100N

A1 = Pi * r^2 (round because diameter is given)

F2 = M*g = 1000*10 = 10000

A2 = Pi* r2 = pi*1^2 (r=1)

so

F1/F2 = A1/A2

100/10000 = pi*r^2/Pi*1

r1= 0.1 (ans.)