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Right choice is (c) If car is MOVING with constant velocity, PA – PB = 0

To explain I WOULD SAY: When the car is moving with constant velocity, points on the same horizontal level will have the same pressure.

So, PA – PB = 0. When the car moves with constant acceleration the pressure difference between those two points will be ρaL, as the pressure difference will be responsible for providing acceleration to the small fluid column of VOLUME L*dA between points A & B (where dA is an area of small element that we think of).

The correct answer is (a) Viscous flow

For EXPLANATION: Bernoulli’s equation can be used for non-viscous, INCOMPRESSIBLE and STEADY laminar flow.

Right choice is (B) False

For EXPLANATION I would say: Velocity can be different at the same horizontal level if the area of the CROSS section at the TWO points is different.This is according to the equation of continuity, A1V1 = A2v2, where A is area and v is velocity.

Correct option is (B) False

For explanation I would say: Coefficient of viscosity is a constant of proportionality for the viscous force EXPRESSION. Viscous force depends on the area of contact and the velocity GRADIENT, and also on the temperature as more temperature of liquid will decrease FRICTION between its layers hence we say that coefficient of viscosity depends on temperature.

Right choice is (c) Pascal

For EXPLANATION I would SAY: The SI unit of pressure is “Pascal”. It is denoted by “Pa”.

1 Pa = 1 N/m^2

It is named after the FAMOUS SCIENTIST Blaise Pascal.

The correct option is (a) Centre

The best explanation: We know that the shear strain rate is v/l, where v is VELOCITY of layer and l is DISTANCE of that layer from layer having zero speedHere, the layer in contact with PIPE WALL will have zero speed.Therefore, the velocity will INCREASE as one goes away from the wall and will be maximum at centre.

Right choice is (d) the extra energy that the molecules at the surface have relative to molecules inside the liquid

To explain I would say: Molecules much below the surface are ATTRACTED by equal forces in all directions, while molecules on the surface have a net force acting on them as they are exposed to air from one side and WATER on another. This net force acting on the surface molecules has a corresponding energy CALLED surface energy.

Right choice is (b) 1.48m/s

The explanation: We should apply Bernoulli theorem between the TOP surface of water and the HOLE.The area of hole is very small when compared to the area of the tank.So, 1/2ρv^2 at the top surface of the tank can be neglected.

P0 + F/AP + ρgh = P0 + 1/2ρv^2

∴ 1000/10 + 1000*10*0.1 = 0.5*1000 *V^2

∴ v = 1.48m/s

The correct answer is (c) Barometer

To explain I WOULD say: A “barometer” is a scientific instrument USED to MEASURE air pressure. The barometer can ALSO be used to measure the altitude of a region because pressure varies with altitude.

Right OPTION is (b) 7.5\(\sqrt{3}\) Pa

To explain I would say: One important thing to keep in mind is that pressure at a point is the NORMAL COMPONENT of force per unit AREA, NOT total force per unit area.

So, here we will take the normal component of 30N force, i.e:

30cos(30°)=15\(\sqrt{3}\).

Press = F/A = 15\(\sqrt{3}\)/2

= 7.5\(\sqrt{3}\) Pa.

The correct choice is (a) Electromagnetic

Explanation: At the contact surface of TWO BODIES (here, fluid layers) molecular bonds are formed. When there is relative motion between them these bonds try to oppose it. This is how friction works. THEREFORE we can say it is an electromagnetic force as molecular bonds are considered to be electromagnetic FORCES.

The correct OPTION is (C) height of hole from liquid

The EXPLANATION: Given that the area of the tank is > > area of hole, we can use the FORMULA V = \(\sqrt{2gh}\). This shows that speed depends only on acceleration due to gravity and height of hole from the surface.

The correct answer is (d) A pressure change at any point in the fluid is transmitted throughout the fluid such that the same change OCCURS everywhere

The best explanation: For EVERY action, there is an equal and opposite reaction – NEWTON’s Third Law

Force is the time rate of change of momentum – Newton’s Second Law

For an ideal GAS, the pressure is directly proportional to temperature and constant volume and mass – Ideal Gas Law

A pressure change at any point in the fluid is transmitted throughout the fluid such that the same change occurs everywhere – Pascal’s Law.

The correct choice is (c) H/2

For explanation: Let the HOLE be at a height x below the top surface.

The DISTANCE of hole from the ground will be H-x.

Speed of efflux ‘v’ = \(\sqrt{2gx}\).

Let the time taken for water to reach the ground be ’t’. H-x = 1/2gt^2.

∴ t = \(\sqrt{2/g(H – x)}\).

For MAXIMUM RANGE, v*t should be maximum.

∴ d(\(\sqrt{2/g(H – x)}\)*\(\sqrt{2gx}\))/dx = 0

∴ d(\(\sqrt{Hx – x^2}\))/dx = 0

∴ (H-2x)/2 \(\sqrt{Hx – x^2}\) = 0

The numerator should be zero but denominator should be non-zero.

∴ H ≠ x (for denominator to be non-zero)

∴ H = 2xOR x = H/2.

The correct choice is (B) False

The best I can explain: Imagine a fluid element with its bottom LAYER having zero velocity and upper layer, at a height ‘h’, having velocity ‘V’.As the fluid moves, the bottom layer stays as it is, while the other layers will move relative to the bottom layer.So, the strain (=v*Δt/h) continuously increases with time.So we talk about strain rate (=v*Δt/h*Δt = v/h) and not about strain.And we say that stress is proportional to strain rate.Therefore the COEFFICIENT of viscosity is the RATIO of stress & strain rate.

The correct OPTION is (c) 15m/s

To explain: We can’t CONSIDER the speed of efflux to be \(\sqrt{2gh}\) as the AREAS are comparable. So, we use Bernoulli theorem between the top of the tank and the hole.Pressure at the top of tank and hole will be same, equal to P0,since both are EXPOSED to the atmosphere.

P0 + ρgH + 1/2ρ \(v_{1}^{2}\) = P0+ 1/2ρ\(v_{2}^{2}\)

∴v2 = \(\sqrt{2(gh + v_{1}^{2}/2)}\)

= \(\sqrt{2(10 * 10 + 25/2)}\)

=15m/s.

The CORRECT answer is (a) Pascal’s Law

To explain I would say: Pascals Law states that a pressure change at any POINT in the FLUID is transmitted THROUGHOUT the fluid such that the same change occurs everywhere. This is employed in HYDRAULIC machines by varying cross-sectional areas at required places.

The CORRECT OPTION is (B) 29.47 m/s

Explanation: At TERMINAL velocity, Mg = viscous force.Therefore, 0.001*10^-3*10 = 6πηrv∴ v = 10^-5/ 6πηr= 10^-5 / ( 6π*1.8 X 10^-5*0.001)= 29.47 m/s.

The CORRECT option is (d) the force decreases and/or area increases

Best explanation: Pressure (P) = Force (F)/Area (A)

From the above equation, we can INFER that the pressure is inversely proportional to the area and directly proportional to the applied force.

Hence, the pressure will decrease when force is DECREASED and/or area is INCREASED.

Right choice is (a) pressure increases

To elaborate: Pressure (P) = FORCE (F)/AREA (A)

From the above equation, we can see that the pressure is inversely proportional to area.

Hence, the pressure will INCREASE when the area is DECREASED.

Correct answer is (a) 110015 PA

The EXPLANATION: The PRESSURE in the bubble will be more than the pressure just outside it by an amount 2S/R.

The pressure just outside the bubble is P0 + ρgh.

Therefore, pressure INSIDE bubble = P0 + ρgh + 2S/R

= 10^5 + (1000*10*1) + (2*0.075/0.01)

= 110015 Pa.

Correct answer is (a) v

The explanation is: According to the EQUATION of continuity, the velocity at B will be the same as that at A since the AREA of the cross section is the same at both points.You may be confused by thinking that gravity will increase its velocity but the pressure will also DECREASE downwards and therefore net effect will be zero change in velocity.

Right option is (B) 0.1141 J

Explanation: Volume of DROP = 4/3πR^2.Let the RADIUS of droplets be ‘r’. Volume of big drop will be equal to volume of 10 droplets.

10*4/3πr^3=4/3πR^3 ⇒ r = 10^1/3 *R.

SURFACE area of big drop = 4πR^2& surface area of 10 droplets = 10 * 4πr^2 = 40πR^2(10^2/3).

Surface energy of big drop = 4πR^2 *S = 4π(0.0025)*0.08 = 0.0025

Surface energy of droplets = 40πR^2(10^2/3) *S = 40π(0.0025)(10^2/3)*0.08 = 0.1166.

Change in surface energy = 0.1166 – 0.0025 = 0.1141 J.

The correct choice is (d) In a given streamline, VELOCITY of a point can vary with time

Easiest EXPLANATION: If we consider a streamline in a pipe of varying diameter we can say that SPEED of different points in that streamline are different. The TANGENT to a streamline gives the direction of velocity at that point, so two streamlines cannot intersect as at the point of intersection we will not be able to draw a single tangent. In case of steady flow across a pipe, there could be streamlines next to each other having different velocities and hence there will be FRICTION between the streamlines which we call viscosity. If flow is unsteady, but not turbulent, the velocity of a point in a streamline can change. For eg: If we slowly increase the speed of a tap flow will be laminar and speed of a point (on a streamline) will increase with time.

Right option is (a) 2S/R

The BEST EXPLANATION: Let the pressure outside the bubble be P1, between the two layers be P2 and pressure inside the bubble be P3.

P2 – P1 = 2S/R

P3 – P2 = 2S/R∴ P3 – P1 = 4S/R

This shows that EXCESS pressure just inside the first layer is 2S/Rwhile excess pressure completely inside the bubble is 4S/R.

Right choice is (a) 2πRS

Best explanation: The diametrical cross section of a sphere will be a circle of radius R.One hemisphere will exert a force of SDL (DL is a SMALL ELEMENT of length along periphery) on dl length.

 Total length = perimeter of circle = 2&7pi;R. Therefore, total force = 2πRS.

Correct choice is (a) True

The best I can explain: A streamline is a curve to which TANGENT at every POINT GIVES the velocity of that point. The flow of water through a BENT pipe can be steady, and when we observe a streamline in it, it will be curved.

Right ANSWER is (c) fluids

For explanation: Pascal’s LAW is VALID for water, gases and even other liquids. HOWEVER, it is not applicable to any other form of MATTER. Hence, we can conclude that Pascal’s Law is valid only for fluids.

Correct answer is (b) False

For explanation: If the tube is of insufficient length then the contact ANGLE CHANGES and doesn’t let water overflow. The SURFACE tension force balances the WEIGHT of water risen.2πrcosθ*S = πr^2 hρg.Here, theta will be different from the known value of contact angle for water and glass tube.

Correct option is (b) 0.1

Explanation: POISE is the C.G.S unit of COEFFICIENT of viscosity.poise = dyne-s/cm^2.1Ns/m^2 = 10^5* 1/10^4 dyne-s/cm^2 = 10 dyne-s/cm^2.

∴ 1 dyne-s/cm^2 = 0.1 Ns/m^2 = 1 poise.

Right choice is (c) Increases for GASES and decreases for liquids

To explain I would say: In the case of liquids when temperature increases, viscosity decreases because it is the result of molecular bonds (ELECTROMAGNETIC forces) between particles which weaken due to random motion brought about by increase in temperature.In the case of gases, the molecules vibrate more randomly, LEADING to more obstruction in the path of bodies TRYING to move through it. And we INTERPRET this increased obstruction as increased viscosity of the gas.

Correct ANSWER is (C) surface energy per unit area

Explanation: Surface tension is defined as force per unit LENGTH or surface energy per unit area.The unit is therefore N/m.Another unit people use is J/m^2 (where J REFERS to joule, the unit of energy).But obviously it is EQUAL to Nm/m^2= N/m.

The correct choice is (d) mass X (velocity)^2/VOLUME

Best explanation: The S.I. unit of pressure is N/m^2.

Work has the unit of NM. Energy/Velocity has the unit of Nm/(m/s)= Ns.

The unit of energy/disp is Nm/m = N.

The unit of mass X (velocity) ^2/Volume is same as that of energy per unit volume becausemass X (velocity)^2 is EQUAL to energy,

which is in TURN equal to Nm/m^3 = N/m^2,therefore this is the correct option.

Correct CHOICE is (a) F/F’ = 1/3

To explain: PRESSURE on first rod (P) = F/A

Pressure on the SECOND rod (P’) = F’/3A

Given;

P = P’

F/A = F’/3A

F/F’ = 1/3.

Correct choice is (b) 2S / Rρg

Best explanation: In the given diagram the surface tension force will be ACTING along the RED tangent. THEREFORE, the force is 2πrcosθ*S.This will be BALANCED by the WEIGHT of water risen in the tube.

 ∴ πr^2 hρg = 2πrcosθ*S

∴ h = 2Scosθ / rρg

= 2S / Rρg.(∵cosθ = r/R)

Correct option is (a) If CONTACT angle is found to be less than 90°, the liquid will have raise ALONG the solid surface

The explanation: A liquid rises or gets depressed along a solid surface such that its surface at that place is perpendicular to the net FORCE. Near the solid and water INTERFACE the particles of fluid are acted upon by forces from solid & liquid particles and also gravity. If the resultant force vector on those fluid particles passes through the solid surface, the surface of fluid has to rise to ensure that net force is perpendicular to its surface. When liquid rises the contact, angle becomes less than 90°. Refer to the diagram given.

Right choice is (c) Conservation of mass

The explanation: The continuity equation is based on the conservation of mass. We consider that FLUID is INCOMPRESSIBLE (constant density) and say that mass of fluid passing through 2 different regions at the same time is the same.

∴ density X Vol1 = density X Vol2.

∴ Vol1 = Vol2.

∴ A1v1Δt = A2v2Δt

∴ A1V1 = A2V2.