Question

3 The
area
of
cross-section of first end of
a U-shaped tube is 0.001 m² and that of the
second and is 1 m2 respectively. On applying
a force on the first and of the tube, a force
of
12000 N was experienced at the
Second end calculate the force exter
excerted on the first end of the tube.

Answer 1

Given:

• The area of cross-section of the first end of the U-shaped tube = 0.001 $m^2$
• The area of cross-section of the second end of the U-shaped tube = 1 $m^2$
• Force exerted on second end = 12000 N

To Find:

• The force exerted on the first end of the tube.

Solution:

Since it is a U-shaped tube, the pressure exerted in it is constant in all directions. (Pascal's Law)

We know that,

Force/Area = constant

Since there are two ends we can write,

$F_1/A_1 = F_2/A_2$ → {equation 1}

Where "$F_1$" is the force exerted on the first end of the tube, "$F_2$" is the force exerted on the second end of the tube, "$A_1$" is the area of cross-section of the first end, "$A_2$" is the area of cross-section of the second tube.

On substituting the given values in equation 1 we get,

⇒ $F_1$/0.001 = 12000/1

On cross-multiplying we get,

⇒ $F_1$ = 12000 × 0.001 {multiplying the terms}

⇒$F_1$ = 12 N

∴ The force exerted on the first end of the tube = 12 N.