Speed of Efflux

Q. A tank, which is open at the top, contains a liquid up to a height $H$. A small hole is made in the side of the tank at a distance $y$ below the liquid surface. The liquid emerging from the hole lands at a distance $x$ from the tank. Which of the following is not correct?

1. The maximum value of $x$ is $H$.
2. $x$ is maximum for $y=\frac{H}{2}$.
3. If $y$ is increased from zero to $H$, $x$ will first increase and then decrease.
4. The maximum value of $x$ will depend on the density of the liquid.

Q.

Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are v₁ and v₂ respectively.

1. 

2. v₁ = v₂.

3. v₁ = 13.6 v₂.

4. v₁ = v₂/13.6.

Q.

There is a small hole near the bottom of an open tank filled with a liquid. The speed of the water ejected does not depends on

1. area of the hole

2. density of the liquid

3. Height of the liquid from the hole

4. acceleration due to gravity

Q.

When a rod is heated but prevented from expanding, the stress developed is independent of

1. Material of the rod

2. Rise in temperature

3. Length of rod

4. None of above

Q.

A uniform steel wire of cross-sectional area $0.20m{m}^2$ is held fixed by clamping its two ends. Find the extra force exerted by each clamp on the wire if the wire is cooled from ${100}^{\circ }C$ to $0^{\circ }C$. Young's modulus of steel = $2.0\times {10}^{11}N/m^2$. Coefficient of linear expansion of steel = $1.2\times {10}^{-5}{/}^{\circ }C$.

1. 480 N

2. 4.8 N

3. 48 N

4. 500 N

Q.

Which of the following arrangements of a wire clamped on two walls will cause an additional stress within the wire?

1. A piece of wire clamped between two clamps is heated up

2. A piece of wire clamped between two clamps is cooled down

3. Both (a) and (b)

4. Neither (a) nor (b)

Q. A wire of length $L_0$ is supplied heat to to raise its temperature by T. If $\gamma$ is the coefficient of volume ex the wire and Y is the young's modulus of the wire then the energy density stored in the wire is

1. 
2. 
3. 
4. 

Q.

There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm (1 atm = ${10}^5$N/$m^2$) then the velocity of water flowing from hole is

1. 

2. 

3. 

4. None of these

Q.

A cylindrical tank has a hole of 1 $c{m}^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 70 $c{m}^3$/sec. then the maximum height up to which water can rise in the tank is

1. 2.5cm

2. 5cm

3. 10cm

4. 0.25cm

Q. A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h/2 and from h/2 to zero is

1. $\sqrt{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\frac{1}{\sqrt{2}-1}$
4. $\sqrt{2}-1$