Class 11 Physics, Chapter 9 (NCERT). 15 questions by concept, 2 with pictures. Open “Show answer” for the answer and why.
How to teach this chapter · Common misconceptions & worked visual for this chapter
An open U-tube has separate water and oil columns above a common interface level. The water column is 8 cm tall and oil density is 800 kg/m³; water density is 1000 kg/m³. What oil-column height balances it?
(c) 10 cm
Equate pressures at the common interface: ρ_water h_water=ρ_oil h_oil. The less dense oil requires a taller column.
A hydraulic press has circular output and input pistons with diameter ratio 4:1. In the ideal equal-height case, what is output force / input force?
(b) 16
Circular area is proportional to diameter squared. The hydraulic force ratio equals the area ratio, so square 4.
A normal force of 180 N acts uniformly on an area of 6 m². What is the pressure?
(c) 30 Pa
Pressure is normal force divided by area. Use P=180/6 pascals.
The manometer contains water of density 1000 kg/m³. Using g=10 m/s², what is gas pressure minus atmospheric pressure for the shown levels?
(a) 2000 Pa
The lower gas-side surface means the gas pressure exceeds atmosphere. The excess is ρgh with h converted from centimetres to metres.
A vessel’s absolute gas pressure is 180 kPa while local atmospheric pressure is 90 kPa. What should a gauge referenced to that atmosphere read?
(a) 90 kPa
Gauge pressure is absolute pressure minus the atmospheric reference. Subtract 90 kPa from 180 kPa.
Water flows steadily through the horizontal pipe shown. Ignore viscosity and treat it as incompressible. How does static pressure at B compare with A?
(a) It is lower at B because the higher speed uses more of the conserved energy per volume.
Continuity makes the speed larger at the smaller area B. At the same height, P+ρv²/2 is constant, so the static pressure decreases.
A viscous liquid flows steadily through a horizontal pipe of uniform area. Its measured pressure falls by 5 kPa over a long segment. How should this be interpreted?
(a) Viscous dissipation requires an energy-loss term; the lossless Bernoulli equation is inapplicable here.
At constant area and density the steady speeds match. The pressure drop supplies energy dissipated by viscosity, an effect excluded from lossless Bernoulli.
Water flows steadily through a pipe with area 20 cm² at speed 3 m/s and then through area 5 cm². Treat water as incompressible. What is its speed in the second section?
(c) 12 m/s
Mass continuity for constant density gives A₁v₁=A₂v₂. A smaller cross-section requires a larger speed.
A large open tank has water depth 10 m. A small side outlet is 34/5 m above the bottom, and both free surface and jet are at atmospheric pressure. With g=10 m/s², neglecting losses and surface speed, what is the jet speed?
(c) 8 m/s
The available head is free-surface height minus outlet height, H−y. Use v=√[2g(H−y)], not the outlet height above the bottom.
For steady laminar flow, use the supplied law Q=πr⁴ΔP/(8ηL). Radius becomes 3 times larger while pressure drop, viscosity and length stay fixed. What is new volume flow rate / old rate?
(b) 81
The supplied Poiseuille law contains the fourth power of radius. The flow change includes the changed velocity profile, not only the area change.
A small sphere of weight 5 mN falls steadily at terminal speed in a viscous liquid. What is true of its acceleration and gravity?
(b) Acceleration is zero; gravity remains nonzero and is balanced by upward forces.
Terminal speed is a constant nonzero velocity. The net force vanishes as drag plus buoyancy balances weight; gravity itself does not vanish.
A plate moves at fixed speed over a stationary plate with a Newtonian liquid between them. Viscosity and area stay fixed, and the velocity profile remains linear. The gap becomes 3 times larger. What is new viscous force / old force?
(c) 1/3
The shear gradient is v/l. At fixed speed, increasing the gap reduces the gradient and hence force by the same factor.
A soap bubble and an air cavity inside liquid have the same radius 1/100 m and surface tension 1/20 N/m. What are their excess pressures above the immediately surrounding medium, respectively?
(b) 20 Pa, 10 Pa
The soap film has two interfaces, giving 4S/r. The air cavity in bulk liquid has one interface, giving 2S/r.
Soap films at the same temperature have identical liquid and movable-edge length. Frame B has 2 times A’s film area because its fixed sides are longer. What is film pull on B’s slider / that on A’s?
(b) 1
Slider force is 2Sl. With the same S and slider length, changing total film area changes stored surface energy but not the slider force.
For the same wetting liquid and acute contact angle in the same gravity, a capillary tube has radius multiplied by 3. Assuming the tube is long enough, what is new equilibrium rise / old rise?
(a) 1/3
Balancing 2πrS cosθ with ρπr²hg gives h=2S cosθ/(ρgr). The rise therefore scales inversely with radius.
Wrong
The wide tank has greater water pressure at the same depth.
Why it feels right. It holds more water.
Right
At a fixed depth, hydrostatic pressure depends on density and depth.
Worked example
