Equation of Continuity

Q.

At Deoprayag (Garhwal, UP) river Alaknanda mixes with the river Bhagirathi and becomes river Ganga. Suppose Alaknanda has a width of 12 m, Bhagirathi has a width of 8 m and Ganga has a width of 16 m. Assume that the depth of water is same in the three rivers. Let the average speed of water in Alaknanda be 20 km h^-1 and in Bhagirathi be 16 km h^-1. Find the average speed of water in the river Ganga.

1. 23 m/s

2. 23 km/hr

3. 46 km/hr

4. 46 m/s

Q.

Water flows through a horizontal tube of variable cross section. The area of cross section at A and B are 4 mm² and 2 mm² respectively. If 1 cc of water enters per second through A, find the speed of water at B?

1. 25 cm/s

2. 50 cm/s

3. 25 mm/s

4. 50 mm/s

Q.

Water enters through end A with a speed v₁ and leaves through end B with a speed v₂ of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward. We have v₁ = v₂ for

1. Case I

2. Case II

3. Case III

4. each case

Q. A iron rod of length 50 cm is joined at an end to an aluminum rod of length 100 cm. All measurements refer to ${20}^{\circ }C$. The coefficients of linear expansion of iron and aluminum are $12\times {10}^{-6}{/}^{\circ }C$ and $24\times {10}^{-6}{/}^{\circ }C$ respectively. The average coefficient of composite system is

1. 
2. 
3. 
4. 

Q. Two rods of length $L_2$ and coefficient of linear expansion ${\alpha }_2$ are connected freely to a third rod of length $L_1$ of coefficient of linear expansion ${\alpha }_1$ to form an isosceles triangle. The arrangement is supported on the knife edge at the midpoint of $L_1$ which is horizontal. The apex of the isosceles triangle is to remain at a constant distance from the knife edge if

1. 
2. 
3. 
4. 

Q.

Solids expand on heating because

1. Kinetic energy of the atoms increases

2. Potential energy of the atoms increases

3. Total energy of the atoms increases

4. The potential energy curve is asymmetric about the equilibrium distance between neighbouring atoms

Q.

The lengths of steel and copper rods are so that the length of the steel rod is 5 cm longer than that of the copper rod at all temperatures, then length of each rod, are ($\alpha$ for copper = $1.7\times {10}^{-5}{/}^{\circ }C$ and $\alpha$ for steel = $1.1\times {10}^{-5}{/}^{\circ }C$) -

1. 9.08 cm; 14.08 cm

2. 9.50 cm; 14.50 cm

3. 9.17 cm; 14.17 cm

4. 9.02 cm; 14.20 cm

Q.

A cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system -

1. x decreases, r and d increase

2. x and r increase, d decreases

3. x, r and d all increase

4. Data insufficient to arrive at a conclusion

Q. You measure the length of a brass rod on a hot July afternoon and on a cool January evening, using the same aluminium scale. To your surprise, you find that the rod length is measured to be smaller on the summer day! How?

1. Aluminium expands more on heating than brass

2. Aluminium expands lesser than brass on heating

3. Brass shrinks on heating

4. None of these

Q.

An iron rod and another of brass, both at ${27}^{\circ }C$ differ in length by ${10}^{-3}m$. The coefficient of linear expansion for iron is $1.1\times {10}^{-5}$${/}^{\circ }C$ and for brass is $1.9\times 10-5$${/}^{\circ }C$. The temperature at which both these rods will have the same length is

1. 0°C

2. 152°C

3. 175°C

4. Data is insufficient