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ICSE Class 9 Physics Question 13 of 19

Pressure in Fluids and Atmospheric Pressure — Question 13

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Question 13

Two cylindrical vessels fitted with pistons A and B of area of cross section 8 cm2 and 320 cm2 respectively, are joined at their bottom by a tube and they are completely filled with water. When a mass of 4 kg is placed on piston A, find : (i) the pressure on piston A, (ii) the pressure on piston B, and (iii) the thrust on piston B.

Answer

(i) As we know,

Pressure (P) = Thrust (F)Area (A)\dfrac{\text {Thrust (F)}}{\text {Area (A)}}

Given,

Force on the narrow piston A = 4 kg

AA = 8 cm 2

AB = 320 cm 2

Substituting the values in the formula above, we get,

PA=48⇒PA=0.5 kg cm−2\text P_\text A = \dfrac{4}{8} \\[0.5em] \Rightarrow \text P_\text A = 0.5 \text { kg cm}^{-2} \\[0.5em]

Hence, PA = 0.5 kg cm-2

(ii) As we know, by the principle of hydraulic machine

Pressure on piston A = pressure on piston B

Hence, PB = 0.5 kg cm-2

(iii) Thrust on piston B is acting in the upward direction, which is given by

Pressure (P) = Thrust (F)Area (A)\dfrac{\text {Thrust (F)}}{\text {Area (A)}}

Substituting the values, we get,

0.5=thrust320⇒thrust=0.5×320⇒thrust=160kgf0.5 = \dfrac{\text{thrust}}{320} \\[0.5em] \Rightarrow \text{thrust} = 0.5 \times 320 \\[0.5em] \Rightarrow \text{thrust} = 160 \text{kgf} \\[0.5em]

Hence, thrust on piston B = 160 kgf