# For each of the statements below, indicate whether the statement is true or false and explain...

## Question:

For each of the statements below, indicate whether the statement is true or false and explain your reasoning.

- The cross-sectional area of a hollow needle is half of the cross-sectional area of the tubing connected to the needle.

- As the fluid flows from the tubing into the needle, the distance traveled per unit time by the fluid particles in the needle will be the same as that in the tubing.

- A 5 kg ball that was initially at rest is rolled down a 3-meter-long slope. As the ball rolls down the slope, it maintains its potential energy.

## Law of Conservation of Energy and Equation of Continuity

Law of conservation of energy is valid in all situations and according to this total energy of any system or object that is the sum of kinetic energy and potential energy is a conserved quantity. As the system or particle evolves in time, one form of energy may get converted into another with total energy remaining constant. Equation of continuity is a conservation law in liquid flow through a tube. It is also an out come of energy conservation. According to the equation of continuity volume rate of flow is a constant through a tube.

## Answer and Explanation:

**a)** The cross sectional area of the hollow needle is half that of the cross sectional area of the tubing connected to the needle.

As the fluid flows from tubing into the needle, the distance traveled per unit time by the fluid particles in the needle will be same as that in the tubing.

**False**

Let {eq}A, \ \ \frac { A } { 2 } {/eq} be the area of cross section of the tubing and needle .

Let {eq}v_1, \ \ v_2 {/eq} be the speed of flow of the liquid in the tubing and in the needle.

Then from equation of continuity we get {eq}A v_1 = \dfrac { A v_2 } { 2 } {/eq}

Therefore speed of the liquid flow in the needle must be {eq}v_2 = 2 v_1 {/eq}

Therefore distance traveled by the fluid particle will be twice as large as that in the tubing in unit time.

**b)**A *5* kg ball that was initially at rest is rolled down a *3* meter long slope.

As the ball rolls down the slope, it maintains its potential energy.

**False**

As the balls rolls down its potential energy gradually gets converted into rotational and linear kinetic energy. So the potential energy is not maintained.

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