Surface Energy

Q.

A 2 kg stone at the end of a string 1 m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m/sec. The tension in the string will be 52 N, when the stone is

1. At the bottom of the circle

2. the string makes an angle of 45 to the vertical

3. At the top of the circle

4. the string is horizontal

Q. 7. A water drop of radius 1 cm is broken into 100Oequal droplets. What would be the gain in surfaceenergy if the surface tension of water is0.075 Nm ?(a) 16.96 x 10 J(c) 4.24 x 10 J\lbrack UK PMT 2015\rbrack(b) 8.48 x 10 J(d) 2.12x 10

Q. A Carnot engine takes 6000 Cal of heat from a reservoir at 627°C and gives it to sink 27°C. The work done by the engine is

Q.

The radii of two soap bubbles are r ₁ and r ₂. In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by

1. r =(r₁ + r₂)/2

2. r =r₁(r₁r₂+r₂)

3. r² =r₁²+r₂²

4. r =r₁+r₂

Q. 67. A hollow sphere of specific gravity 2, floats whencompletely immersed in water. If the volume of thesphere is V, then the volume of cavity is(a) V/8(c) V/4(b) V/3(d) V/2

Q. Calculate the surface energy of ring floating on the liquid surface .surface tension of liquid is 75n/m and the area of the ring is 0.04msq.

Q. a horizontal circular loop of wire of radius 0.02 m is lowered into crude oil form film . The force due to the surface tension of the liquid is 0.0113 N . Calculate the surface tension of crude oil

Q. A number of water droplets each of radius r coalesce to form a drop of radius R. Assuming the whole of the energy liberated due to coalescence goes into heating the drop, the rise in the temperature dθ is :-

Q.

The work done in blowing a soap bubble of radius $0.2m$, given that the surface tension of soap solution is $60\times {10}^{-3}N/m$ is

1. $192\pi \times {10}^{-4}J$

2. $96\pi \times {10}^{-4}J$

3. $8\pi \times {10}^{-4}J$

4. $124\pi \times {10}^{-4}J$

Q. A solid cylinder of height h and cross sectional area a and density 1.40 multiply 1000 kilogram permetre cube is immersed completely in a mixture of liquid such that it floats with its Axis vertical are the liquid liquid interface with length 3 h/4 intense liquid that is less than other as shown in the figure the lesser than solid liquid is opened atmospheric pressure p. if the density of lesser denser liquid is 1000 kilogram per metre cube then the density of denser liquid will be

Q. The surface energy of a drop of water of radius $r$ is proportional to:

1. $r^3$
2. $r^2$
3. $r$
4. $\frac{1}{r}$

Q. A body of volume V and density p is initially submerged in a non-viscous liquid of density σ(>p). If it is rises by itself through a height h in the liquid. Its kinetic energy will (a) increase by hV (σ -p)g (b) increase by hV (p + σ)g (c) decrease by hVpg/σ (d) increase by hVpg

Q. A drop of liquid of diameter $2.8\text{mm}$ break up into $216$ identical drops. What is the approximate change in energy of bigger drop?
(Given: Surface tension of liquid, $T=75\text{dyne/cm}$)

1. $25\pi \text{erg}$
2. $29.4\pi \text{erg}$
3. $32\pi \text{erg}$
4. $28\pi \text{erg}$

Q.

The volume of a spherical body is decreased by 10^-3% when it is subjected to pressure of 40 atmospheres. Find the bulk modulus of body.
(1 atm = 1.01 x 10³ N/m²).

1. 4.04 x 10⁶ N/m²

2. 4.04 x 10² N/m²

3. 4.04 x 10³ N/m²

4. 4.04 x 10¹¹ N/m²

Q. A rectangular film of liquid is extended from $(4\text{cm}\times 2\text{cm})$ to $(5\text{cm}\times 4\text{cm})$. If the work done is $3\times {10}^{-4}\text{J}$, then value of the surface tension of the liquid is

1. $0.250{\text{N m}}^{-1}$
2. $0.125{\text{N m}}^{-1}$
3. $0.275{\text{N m}}^{-1}$
4. $0.325{\text{N m}}^{-1}$

Q. Two drops of equal radii coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?

1. $2^{1/3}:2$
2. $2^{1/2}:2$
3. $2^{2/3}:1$
4. $2:1$

Q. 12. If speed and density of a liquid coming out of acylindrical pipe is increased to three times, then theforce required to hold the pipe becomes(1) 3 times(2) 9 times227 times(4) 6 times

Q. Water rises to a height of 10 cm in a capillary tube and mercury falls to a depth of 3.42 cm in the same capillary tube. If the density of mercury is13.6 kg/m^3 and angle of contact is 135^°, the ratio of surface tension for water and mercury is (angle of contact for water and glass is 0^°). (1) 1:0.5, (2) 1:3, (3) 1:6.5, (4) 1.5:

Q.

A drop of liquid of diameter 2.8 mm breaks up into 125 identical drops.

The change in energy is nearly (S.T. of liquid =75 dynes/cm)

1. 19 erg

2. Zero

3. 46 erg

4. 74 erg

Q. The bulk modulus of a spherical object is B. ifit is subjected to uniform pressure p, the fractional decrease in radius is 1)p/B 2)B/3P 3)3P/B 4)P/3

Q. Determine the volume contraction of a solid copper cube, $10cm$ on an edge, when subjected to a hydraulic pressure of $7.0\times {10}^{6}Pa$. (Bulk modulus of copper, $B=140\times {10}^{9}Pa$)

Q. Calculate the energy released when $1000$ small water drops each of same radius ${10}^{-7}\text{m}$ coalesce to form one large drop. The surface tension of water is $5\times {10}^{-2}\text{N/m}$.

1. $5\pi \times {10}^{-12}\text{J}$
2. $4.2\pi \times {10}^{-12}\text{J}$
3. $3.6\pi \times {10}^{-12}\text{J}$
4. $1.8\pi \times {10}^{-12}\text{J}$

Q.

n drops of liquid each with surface energy E, join to form a single drop. In this process

1. No energy will be absorbed

2. Energy absorbed is E(n - n^2/3)

3. Energy released will be E(n - n^2/3)

4. Energy released will be E(2^2/3 - 1)

Q. A certain number of spherical drops of a liquid of radius $r$ each, coalesce to form a single drop of radius $R$ and volume $V$. If $T$ is the surface tension of the liquid, then

1. Energy $=3VT(\frac{1}{r}+\frac{1}{R})$ is released
2. Energy $=3VT(\frac{1}{r}+\frac{1}{R})$ is absorbed
3. Energy $=3VT(\frac{1}{r}-\frac{1}{R})$ is released
4. Energy $=3VT(\frac{1}{r}-\frac{1}{R})$ is absorbed

Q. A box contain equal number of molecules of hydrogen and oxygen. If there is a line hole in the box, then which gas leakes more rapidly?

1. Can't say
2. Hydrogen gas
3. Oxygen gas
4. Both leak at equal rates

Q. When water droplets merge to form a bigger drop, energy is.

1. liberated
2. absorbed
3. neither liberated nor absorbed

Q. Determine the energy stored in the surface of a soap bubble of radius $2.1\text{cm}$ if its surface tension is $4.5\times {10}^{-2}\text{N/m}$.

1. $3.6\pi \times {10}^{-4}\text{J}$
2. $0.6\pi \times {10}^{-4}\text{J}$
3. $1.6\pi \times {10}^{-4}\text{J}$
4. $2.6\pi \times {10}^{-4}\text{J}$

Q. Two drops of equal radii coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?

1. $2^{1/3}:2$
2. $2^{1/2}:2$
3. $2^{2/3}:1$
4. $2:1$

Q. Work done on a liquid drop to increase its radius from $3\text{cm}$ to $5\text{cm}$ is $\pi \times {10}^{-4}\text{J}$. Find the surface tension of liquid.

1. $\frac{1}{8}\text{N/m}$
2. $\frac{1}{4}\text{N/m}$
3. $\frac{1}{64}\text{N/m}$
4. $\frac{1}{32}\text{N/m}$

Q. A mercury drop of radius $1\text{cm}$ is sprayed into ${10}^6$ droplets of equal size. Calculate the energy expended ( in $\text{mJ}$ upto two decimals) if surface tension of mercury is $35\times {10}^{-3}\text{N/m}$.