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1.

A film of water is formed between two straight parallel wires of length 10 cm each separated by `0.5cm` If their separation is increased by `1mm` while still maintaining their parallelism, how much work will have to be done (Surface tension of water `=7.2xx10^-2(N)/(m)`)A. `7.22xx10^-6Joule`B. `1.44xx10^-5joule`C. `2.88xx10^-5joule`D. `5.76xx10^-5joule`

Answer» Correct Answer - B
Increment in area of soap film`=A_2-A_1`
`2xx[(10xx0.6)-(10xx0.5)]xx10^-4=2xx10^-4m^2`
Work done `=TxxtriangleA`
`=7.2xx10^-2xx2xx10^-4=1.44xx10^-5J`
2.

A ball falling in a lake of depth `200 m` shows a decrease of `0.1% ` in its volume at the bottom. The bulk modulus of elasticity of the material of the ball is (take `g = 10 ms^(-2)`)A. `10^8`B. `2xx10^8`C. `10^9`D. `2xx10^9`

Answer» Correct Answer - D
`K=(triangleP)/((triangleV)/(V))=(hrhog)/((triangleV)/(V))=(200xx10^3xx10)/((0.1)/(100))=2xx10^9`
3.

If pressure at half the depth of a lake is equal to 2//3 pressure at the bottom of the lake then what is the depth of the lake ?A. `10m`B. `20m`C. `60m`D. `30m`

Answer» Correct Answer - B
Pressure at half depth`=P_0+(h)/(2)dg`
Pressure at the bottom`=P_0+hrhog`
According to given condition
`P_0+(h)/(2)dg=(2)/(3)(P_0+hdg)`
`implies3P_0+(3h)/(2)dg=2P_0+2hdg`
`impliesh=(2P_0)/(dg)=(2xx10^5)/(10^3xx10)=20m`
4.

The work per unit volume to stretch the length by `1%` of a wire with cross sectional area of `1mm^2` will be. `[Y=9xx10^(11)(N)/(m^2)`]A. `9xx10^11J`B. `4.5xx10^7J`C. `9xx10^7J`D. `4.5xx10^11J`

Answer» Correct Answer - B
`U=(1)/(2)xxYxx("strain")^2=(1)/(2)xx9xx10^11xx((1)/(100))^2`
`=4.5xx10^7J`
5.

The radii of the two columne is U-tube are `r_(1)` and `r_(2)(gtr_(1))`. When a liquid of density `rho` (angle of contact is `0^@))` is filled in it, the level different of liquid in two arms is h. The surface tension of liquid is `(g=` acceleration due to gravity)A. `(rho gh r_(1)r_(2))/(2(r_(2) - r_(1)))`B. `(rho gh (r_(2) - r_(1)))/(2r_(1) r_(2))`C. `(2 (r_(2) - r_(1)))/(rho gh r_(1) r_(2))`D. `(rho gh)/(2(r_(2) - r_(1)))`

Answer» Correct Answer - A
6.

A long glass capillary (radius R) is taken out of liquid (surface tension S and density `rho`) in vertical position. Angle of contact everywhere is zero. Atmospheric pressure is `P_(0)`. It is observed that the capillary retains some liquid. The length of liquid column retained in the capillary isA. `(3 S)/(rho Rg)`B. `(2S)/(rho Rg)`C. `(4S)/(rho Rg)`D. zero

Answer» Correct Answer - B
7.

A long glass capillary (radius R) is taken out of liquid (surface tension S and density `rho`) in vertical position. Angle of contact everywhere is zero. Atmospheric pressure is `P_(0)`. It is observed that the capillary retains some liquid. The radius of curvature of meniscus at the bottom of tube isA. BB. `oo`C. `R//2`D. `R//3`

Answer» Correct Answer - A
8.

A capillary tube of radius r is lowered into a liquid of surface tension T and density `rho`. Given angle of contact `=0^(@)`. What is the potential energy acquired by the liquid in the capillary?A. `(pi T^(2))/(2 rho g)`B. `T^(2)/(2 rho g)`C. `T^(2)/(rho g)`D. `(2 pi T^(2))/(rho g)`

Answer» Correct Answer - D
9.

A capillary tube of radius r is lowered into a liquid of surface tension T and density `rho`. Given angle of contact `=0^(@)`. The work done by surface tension will beA. `(pi T^(2))/(rho g)`B. `(4 pi T^(2))/(rho g)`C. `(T^(2))/(rho g)`D. `(2T^(2))/(rho g)`

Answer» Correct Answer - B
10.

A cylinder of mass m and density `rho` hanging from a string is lowered into a vessel of cross-section area s containing a liquid of density `sigma (lt rho)` unit it is fully immersed. The increase in pressure at the bottom of the vessel isA. `(m rho g)/(sigma s)`B. `(mg)/(s)`C. `(m sigma g)/(rho s)`D. zero

Answer» Correct Answer - C
11.

Figure here shows the vertical cross-section of a vessel filled with a liquid of density `rho`. The normal thrust per unit area on the walls vessel at point. `P`, as shown, will be A. `h rho g`B. `H rho g`C. `(H - h) rho g`D. `(H - h) rho g cos theta`

Answer» Correct Answer - A
12.

A cylindrical vessel contains a liquid of density `rho` up to height `h`. The liquid is closed by a piston of mass `m` and area of cross section `A`. There is a small hole at the bottom of the vessel. The speed `v` with which the liquid comes out of the hole is A. `sqrt(2gh)`B. `sqrt(2(gh + (mg)/(rho A)))`C. `sqrt(2(gh + (mg)/(A)))`D. `sqrt(2gh + (mg)/(A))`

Answer» Correct Answer - B
13.

A cylindrical vessel of area of cross-section A is filled with water to a height H. It has capillary tube of length l and radius r fitted horizontally at its bottom. If the coeffiecient of viscosity of water is `eta`, then time required in which level will fall to a height `(H)/(2)` is (density of water is `rho`)A. `(eta//r^(2))/(4Arho)1n (2)`B. `(4 eta//r^(4))/(pi g A rho) ln ((1)/(2))`C. `(8 eta//A)/(rho pi g r^(4)) ln (2)`D. `(4 Heta//rho)/(pi g r^(4))ln (2)`

Answer» Correct Answer - C
14.

A block is fully submerged in a vessel filled with water by a spring attached to the bottom of the vessel. In equilibrium position spring is compressed. If the vessel now moves downwards with an acceleration `a(lt g)`. What happens to the length of the spring.? A. will become zeroB. may increase, decrease or remain constantC. will decreaseD. will increase

Answer» Correct Answer - D
15.

A glass capillary of length l and inside radius `r(r lt lt l)` is submerged vertically into water. The upper end of the capillary is scaled. The atmospheric pressure is `p_(0)`. To what length h has the capillary to be submerged to make the water levels inside and outside the capillary coincide. Assume that temperature of air in the capillary remains constant. (given, surface tension of water = T, angle of contact between glass water interface `= 0^(@)`) A. `(l)/(1+(p_(0)r)/(T))`B. `(l)/(1+(p_(0)r)/(2T))`C. `(l)/(1+(p_(0)r)/(4T))`D. `(l)/(1+(2p_(0)r)/(T))`

Answer» Correct Answer - B
16.

Some liquid is filled in a cylindrical vessel of radius R. Let `F_(1)` be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side R. Let `F_(2)` be the force applied by the liquid on the bottom of this new vessel. (Neglect atmosphere pressure). ThenA. `F_(1) = pi F_(2)`B. `F_(1) = (F_(2))/(pi)`C. `F_(1) = sqrt(pi)F_(2)`D. `F_(1) = F_(2)`

Answer» Correct Answer - D
17.

A thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out . The frame is comletely covered with the film. When the portion `A` puntured with a pin The thread.A. Becomes concave towards `A`B. Becomes convex towards `A`C. Remains in the initial positionD. Either (a) or (b) depensing on the size of `A` w.r.t. `B`

Answer» Correct Answer - A
Because film tries to cover minimum surface area.
18.

Three point masses are at the corners of an equilateral traingle of side `r`. Their separations do not change when the system rotates about the centre of the triangle. For this, the time period of rotation must be proportional toA. `a^(3//2)`B. aC. mD. `m^(-1//2)`

Answer» Correct Answer - A::D
19.

A wooden cube floating in water supports a mass 0.2 kg on its top. When the mass is removed the cube rises by 2cm. What is the side legnth of the cube ? Density of water `= 10^3 kg//m^3`A. 6 cmB. 12 cmC. 8 cmD. 10 cm

Answer» Correct Answer - D
20.

A vertically jet of water coming out of a nozzle with velocity `20 m//s` supports a plate of mass M stationary at a height `h = 15 m`, as shown in the figure. If the rate of water flow is 1 litre per second, the mass of the plate is (Assume the collision to be perfectly inelastic). A. 1kgB. `sqrt(2) kg`C. 2kgD. 4kg

Answer» Correct Answer - A
21.

When the temperature increases the viscosity ofA. gases decreases and liquids increasesB. gases increases and liquids decreasesC. gases and liquids increasesD. gases and liquids decreases

Answer» Correct Answer - B
Viscosity of a liquid decreases with increase in temperature whereas vicosity of gases increases with increase in temperature.
22.

If a spring extends by `x` on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)A. `(T^2)/(2x)`B. `(T^2)/(2k)`C. `(2x)/(T^2)`D. `(2T^2)/(k)`

Answer» Correct Answer - B
`U=(F^2)/(2K)=(T^2)/(2K)`
23.

A metal ball `B_(1)` (density `3.2g//"cc")` is dropped in water, while another metal ball `B_(2)` (density `6.0g//"cc")` is dropped in a liquid of density `1.6g//"cc"`. If both the balls have the same diameter and attain the same terminal velocity, the ratio of viscosity of water to that of the liquid isA. `2.0`B. `0.5`C. `4.0`D. indeterminate due to insufficient data

Answer» Correct Answer - B
`v_(t1)_=v_(t2)`
`(2)/(9)g(r^2)/(n_w)[sigma_1-rho_w]=(2)/(9)g(r^2)/(n_1)(sigma_2-rho_1)`
`implies(n_w)/(n_1)=(sigma_1-rho_w)/(sigma_2-rho_1)=(3.2-1)/(6-1.6)=(1)/(2)`
24.

A mass `m` is suspended from a wire . Change in length of the wire is `Deltal`. Now the same wire is stretched to double its length and the same mass is suspended from the wire. The change in length in this case will become (it is suspended that elongation in the wire is within the proportional limit)A. `Delta l`B. `2 Delta l`C. `4 Delta l`D. `8 Delta l`

Answer» Correct Answer - C
25.

A small steel ball falls through a syrup at a constant speed of `10cms^-1`. If the steel ball is pulled upwards with a force equal to twice its effective weight, how fast will it move upwards?A. 1.0 m/sB. 2.0 m/sC. 0.5 m/sD. zero

Answer» Correct Answer - A
26.

A rain drop starts falling from a height of `2km`. If falls with a continuously decreasing acceleration and attains its terminal velocity at a height of `1km`. The ratio of the work done by the gravitational force in the first halt to that in the second half of the drops journey isA. `1:1` and the times of fall of the drop in the two haves is `a:1` (where `agt1`)B. `1:1` and the times of fall of the drop in the two halves is `a:1` (where `alt1`)C. `a:1` (where `agt1`) and the times of fall of the drop is the two halves is `1:1`D. `a:1` (where `alt1`) and the times of fall of the drop in the two halves is `1:1`

Answer» Correct Answer - A
Taking `g` constant, work done in both the cases is `-mgxx(1000)` since the maximum velocity of the journey is attained at a height of `1km`, and the second half journey is travelled by max. velocity the time taken for second half journey will be less.
27.

A rain drop radius `0.3mm` falling vertically downwards in air has a terminal velocity of `1(m)/(s)` The viscosity of air is `18xx10^-5` poise. The viscous force on the drop isA. `101.73xx10^-4den e`B. `101.73xx10^-5dyn e`C. `16.95xx10^-5den e`D. `16.95xx10^-4dyn e`

Answer» Correct Answer - A
Viscous force`=6pietarv=6pixx18xx10^-5xx0.03xx100`
`=101.73xx10^-4` deyne
28.

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity `(v)` of the pebble as a function of time `(t)`A. B. C. D.

Answer» Correct Answer - C
When the pebble is falling through the viscous oil the viscous force is `F=6pietarv` where `r` is radius of the pebble, `v1` is instantaneous speed, `eta` is coefficient of viscosity. As the force is variable, hence acceleration is also variable so `v-t` graph will not be straight line first velocity increases and then becomes constant known as terminal velocity.
29.

A wire suspended vertically from one of itsends is strached by attached a weight of `200 N` to the lower end . The weight streches the wire by `1 mm` . Then the elastic energy stored in the wire isA. `0.1J`B. `0.2J`C. `10J`D. `20`

Answer» Correct Answer - A
`U=(1)/(2)xxFxxl=(1)/(2)xx200xx10^-3=0.1J`
30.

A spherical liquid drop of radius `R` is divided into eight equal droplets. If the surface tension is `T`, then the work done in this process will beA. `2piR^2T`B. `3piR^2T`C. `4piR^2T`D. `2piRT^2`

Answer» Correct Answer - C
Radius of the larger drop `=R`
Suppose radius of the droplets `=r`
Since, volume will be remain constant,
`(4)/(3)piR^3=8xx(4)/(3)pir^2`
[`because` No. of droplets`=8pixx(0.01)xx75`
work done`=`(increase in surface area)`xx`Surface tension
`=[84pi((R )/(2))^2-4piR^2]xxT`
`=(8piR^2-4piR^2)xxT=4piR^2T`
31.

A mercury drop of radius 1 cm is broken into `10^6` droplets of equal size. The work done is `(T=35xx10^-2(N)/(m)`)A. `4.35xx10^-2J`B. `4.35xx10^-3J`C. `4.35xx10^-6J`D. `4.35xx10^-8J`

Answer» Correct Answer - A
Initial radius of drop,
`R=1cm1xx10^-2m`
suppose, `r` is the radius of droplets
since, volume will be remain constant.
`(4)/(3)piR^3=10^6xx(4)/(3)pir^3`
[since, number of droplets`=10^6`]
`r=(1xx10^-2)/(10^2)`
Increase in surface area,
`triangleS=10^6xx4pir^2-4piR^2`
`=10^6xx4xxpixx10^-8-4pixx10^-4`
`=4xx9.9xxpixx10^-3`
Work done `=`increase in surface area `xx` Surface tension.
`=4xx9.9xxpixx10^-3xx35xx10^-2`
`=4.35xx10^-2J`
32.

An annular disc of radius `r_(1 )= 10 cm` and `r_(2) = 5 cm` is placed on a water surface. Find the surface tension force on the disc if we want to pull it from water surface. Take coefficient of surface tension as `sigma= 7 xx10^(-3) N//m, g = 10 ms^(-2)`. A. `6782.4dune`B. `67.82dyne`C. `678.24dyne`D. none of these

Answer» Correct Answer - A
`F=2pir_1T+F=2pir_2T`
`=(2pi(r_1+r_2)T`
`=2xx3.14(10+5)(72)=6782.4` dyne
33.

A paper disc of radius `R` from which a hole of radius `r` is cut out is floating in a liquid of the surface tension `S`. The force on the disc due to the surface tension isA. `T.3piR`B. `T.2pi(R+r)`C. `T.4pi(R+r)`D. `T.2pi(R-r)`

Answer» Correct Answer - B
Effective length `=2pir+2piR`
34.

A wire of mass `1g` is kept horizontally on the surface of water. The length of the wire that does not break the surface film is (surface tension of water is `70dynecm^-1`)A. `3cm`B. `4cm`C. `7cm`D. `14cm`

Answer» Correct Answer - C
`2lsigma=1xx980` or `l=(980)/(2xx70)=7cm`
35.

A rectangular metal plate has dimensions of `10cmxx20cm`. A thin film of oil separates the plate from a fixed horizontal surface. The separation between the rectangular plate and the horizontal surface is `0.2mm`. An ideal string is attached to the plate and passes over an ideal pulley to a mass `m`. When `m=125gm`, the metal plate moves at constant speed of `5(cm)/(s)`, across the horizontal surface. Then the coefficient of viscosity of oil in `(dyne-s)/(cm^2)` is (Use `g=1000(cm)/(s^2)`)A. 5B. 25C. 2.5D. 50

Answer» Correct Answer - C
The coefficient of viscosity is the ration of tangential stress on top surface of film (exerted by block) to that of velocity gradient (vertically downwards) of film. Since mass `m` moves with constant velocity, the string exerts a force equal to `mg` on plate towards right. Hence oil shall exert tangential force `mg` on plate towards left.
`eta=((F)/(A))/(((v-0))/(trianglex))=((125xx100)/(10xx20))/(((5-0))/(0.2))`
`=2.5(dyn e)/(cm^2)`
36.

A liquid is filled in a spherical container of radius R up to a height `h`. At this position the liquid surface at the end is also horizontal. The contact angle is

Answer» Correct Answer - B
37.

Figure shows water filled in a symmetrical container. Four pistons of equal area `A` are used at the four openings to keep the water in equilibrium. Now an additional force `F` is applied at each piston. The increase in the pressure at the centre of the container due to this addition is A. `(F)/(A)`B. `(2F)/(A)`C. `(4F)/(A)`D. 0

Answer» Correct Answer - A
38.

A 5 metre long wire is fixed to the ceiling. A weight of `10kg` is hung at the lower end and is `1metre` above the floor. The wire was elongated by `1mm`. The energy stored in the wire duw to streching isA. zeroB. `0.05joule`C. `100joule`D. `500joule`

Answer» Correct Answer - B
`W=(1)/(2)xxFxxL=(1)/(2)mgl`
`=(1)/(2)xx10xx10xx1xx10^-1=0.05J`
39.

The U-tube shown has a uniform cross-section. A liquid is filled in the two arms up to heights `h_(1)` and `h_(2)`, and then the liquid is allowed to move. Neglect viscosity and surface tension. When the levels equalize in the two arms, the liquid will A. be at restB. be moving with an acceleration of `g((h_(1)-h_(2))/(h_(1)+h_(2)+h))`C. be moving with a velocity of `(h_(1) - h_(2)) sqrt((g)/(2(h_(1)+h_(2)+h)))`D. exert a net force to the right on the tube

Answer» Correct Answer - C
40.

An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one thrid of volume of water was spilled out. The acceleration wasA. g/3B. 2g/3C. g/2D. g/4

Answer» Correct Answer - B
41.

A small sphere falls from rest in a viscous liquid. Due to friction, heat is produced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.A. `r^4`B. `r^3`C. `r^5`D. `r^2`

Answer» Correct Answer - C
Rate of heat produced `=` power loss against vicous force
`implies(dQ)/(dt)=F_vxxv_T`
where the terminal velocity `v_T=(2r^2)/(9eta)(rho-sigma)g`
and viscous force `F_v=6pietarv_T`
Hence `(dQ)/(dt)=7pietarv_Txxv_T` or `v_Talphar^2`
`implies(dQ)/(dt)proprv_T^2` but `v_Tpropr^2`
Hence `(dQ)/(dt)propr^5`
42.

A non viscous inconpressible liquid is flowing from a horizontal pipe of non-uniform cross section as shown, Choose the correct option

Answer» Correct Answer - A::B::C
43.

A cubical block of side `a` and density `rho` slides over a fixed inclined plane with constant velocity `v`. There is a thin film of viscous fluid of thickness `t` between the plane and the block. Then the coefficient of viscosity of the thin film will be: (Acceleration due to gravity is g)A. `(rhoagtsintheta)/(v)`B. `(rhoagt^2sintheta)/(v)`C. `(v)/(rhoagtsintheta)`D. none of these

Answer» Correct Answer - A
Viscous force `=mgsintheta`
`etaA(v)/(t)=mgsintheta` or `etaa^2(v)/(t)=a^2rhogsintheta`
`eta=(trhogsinthetaa)/(v)`
44.

When a capillary tube is dipped in water, water rises upto `8cm` in the tube. What happends when the tube is pushed down such that its end is only `5cm` above outside water level?A. The radius of the meniscus increases and therefore water does not overflow.B. The radius of the water meniscus decreases and therefore does not overflowC. The water forms a droplet on top of the tube but does not overflowD. The water start overflowing.

Answer» Correct Answer - A
`h=(2sigmacostheta)/(rrhog)` or `h=(2sigmacostheta)/((Rcostheta)rhog)`
or `h=(2sigma)/(Rrhog)` or `hR=`constant
If `h` decreases, the radius of curvature of the meniscus increases.
45.

A soap bubble of radius `r` is placed on another bubble of radius `2r`. The radius of the surface common to both the bubbles isA. `(2r)/(3)`B. `3r`C. `2r`D. `r`

Answer» Correct Answer - C
46.

A cable that can support a load of 800 N is cut into two equal parts. The maximum load that can be supported by either part isA. 100 NB. 400 NC. 800 ND. 1600 N

Answer» Correct Answer - C
Breaking stress does not depend upont the length of the cable.
47.

A material has normal density `rho` and bulk modulus `K`. The increase in the density of the material when it is subjected to an external pressure `P` from all sides isA. `(P)/(rhoK)`B. `(K)/(rhoP)`C. `(rhoP)/(K)`D. `(rhoK)/(P)`

Answer» Correct Answer - C
`(rho^(`))/(rho)=`((M)/(V-triangleV))/((M)/(V))=(V)/(V-triangleV)`
or `(rho^(`))/(rho)=V(V-DeltaV)^(-1)`
or `(rho^(`))/(rho)=1+(triangleV)/(V)`
(Using Binomial Theoram)
or `(triangleV)/(V)=(rho^(`))/(rho)-1` or `(triangleV)/(V)=(rho^(`)-rho)/(rho)`
`K=(triangleP)/((triangleV)/(V))=(rho triangleP)/(rho^(`)-rho)` or `rho^(`)-rho=(rho triangleR)/(K)`
but `triangleP=P` (given)
`thereforerho^(`)-rho=(rhoP)/(K)`
48.

The volume change of a solid copper cube 10 cm on an edge, when subject to a pressure of 7 Mpa is (Bulk modulus of copper `=140GPa`)A. `5xx10^-2cm^3`B. `10xx10^-2cm^3`C. `15xx10^4cm^3`D. `20xx10^-2cm^3`

Answer» Correct Answer - A
Here, `L=10cm=10xx10^-2m`
`P=7MPa=7xx10^6Pa`
`B=140GPa=140xx10^9Pa`
As `B=(P)/((triangleV)/(V))`
`triangleV=(PV)/(B)=(PL^3)/(B)=((7xx10^6Pa)(10xx10^-2m)^3)/(140xx10^9Pa)`
`=5xx10%-8m^3=5xx10^-2cm^3`
49.

The compressibility of water is `6xx10^-10N^-1m^2`. If one litre is subjected to a pressure of `4xx10^7Nm^-2`, The decrease in its volume isA. 10 ccB. 24 ccC. 15 ccD. 12 cc

Answer» Correct Answer - B
Bulk modulus `B=-(P)/((DeltaV//V))`
`-ve` sign shows that with a increase in pressure, a decrease in volume occurs.
Compressibility, `K=(1)/(2)=-(triangleV)/(PV)`
Decrease in volume, `triangleV=PVK`
`=4xx10^7xx1xx6xx10^-10`
`=24xx10^-3litre`
`=24xx10^(-3)10^3cm^3=24c c`
50.

The compressibility of water is `4xx10^-5` per unit atmospheric pressure. The decrease in volume of 100 cubic centimetre of water under a pressure of 100 atmosphere will beA. 0.4 ccB. `4xx10^-5cc`C. `0.025cc`D. `0.004cc`

Answer» Correct Answer - A
`((triangleV)/(V))/(triangleP)impliestriangleC=CtrianglePxxV`
`=4xx10^-5xx100xx100=0.4c c`