Properties of Solids and Liquids

37 solved questions 2 tests

Ask a question

Take chapter test ← Previous Next chapter →

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature… Answer: 3. 5/3 Key idea: in steady state the same heat current flows through all three rods, so kA Δ T/l is equal for each. With equal A and... Heat transfer: conduction, convection, radiation 1 answer
A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density ρ and takes a spherical shape of radius R. When the gas is allowed to flow freely out… Answer: 3. a=-1/2,α=-1/2,β=-1,γ=1/2,δ=7/2 Key idea: the excess pressure inside the balloon is proportional to S/r (it is 4S/r in the standar... Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise 1 answer
Consider a water tank shown in the figure. It has one wall at x = L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes angle θ_0(θ_0 1) with the x-axis at x = L.… Answer: 2. d²y/dx²=ρ g/Sy Key idea: the surface tension pulls the curved surface so that, for each small piece, the net vertical force balan... Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise 1 answer
A metallic bar of Young's modulus, 0.5×10^11 N m^-2 and coefficient of linear thermal expansion 10^-5 ^°C^-1, length 1 m and area of cross-section 10^-3 m^2 is heated from 0^°C to 100^°C without expansion or bending. The compressive force developed i… Answer: 3. 50×10³ N Key idea: If the bar is not allowed to expand, the thermal strain αΔ T is cancelled by a compressive strain, so a stress... Heat, temperature and thermal expansion 1 answer
The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are 8×10^8 N m^-2 and 2×10^11 N m^-2, is : Answer: 2. 4 mm Key idea: The largest stress the wire can bear without permanent change is the elastic limit. Use Y=stress/strain . Strain =... Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli 1 answer
A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 Nm^-1, then the excess force required to take it away from the surface is : Answer: 2. 19.8 mN Key idea: The surface-tension force acts along the line of contact between the disc and the water, which is the circumfer... Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise 1 answer
The venturi-meter works on : Answer: 3. Bernoulli's principle A venturi-meter measures the flow speed of a liquid in a pipe. In the narrow part the speed is higher and t... Bernoulli's principle and applications 1 answer
The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly : (surface tension of soap solution =0.03 N m^-1) Answer: 4. 3.01×10⁻⁴ J A soap bubble has two surfaces (inner and outer), so the energy needed equals surface tension times total area 2×4π r... Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise 1 answer
Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is : Answer: 3. W/A The wire is in equilibrium under the weight W at the free end (the wire's own weight is neglected). The tension at every cros... Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli 1 answer
Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.Reason (R) : A coil spring of copper… Answer: 4. (A) is true but (R) is false Assertion: when a spring is stretched, the wire of the coil is mainly twisted, which is a shear defo... Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli 1 answer
If a soap bubble expands, the pressure inside the bubble : Answer: 2. decreases Excess pressure inside a soap bubble is Δ P=4S/r , so it is inversely proportional to the radius. When the bubble expan... Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise 1 answer
A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is : Answer: 3. B A ball dropped in a viscous liquid starts with acceleration g . As speed grows, viscous drag rises, so the acceleration falls t... Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity 1 answer
A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is : Answer: 2. 13/5t Key idea: Newton's law of cooling in the average-temperature form: Δ T/t=k(T_avg-T₀) . First case: 10/t=k(85-20)=65k⇒ k=2/1... Heat transfer: conduction, convection, radiation 1 answer
The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be : Answer: 1. Mg/2 Key idea: at constant (terminal) velocity the net force is zero: weight = buoyancy + viscous force. Volume of ball V=M/d . B... Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity 1 answer
A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L_1 when mass M is suspended from its free end. The expression for Young's modulus is : Answer: 4. MgL/A(L₁ - L) Young's modulus Y=stress/strain . Stress =Mg/A Strain =L₁-L/L , since the extension is L₁-L and the original length... Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli 1 answer
The quantities of heat required to raise the temperature of two solid copper spheres of radii r_1 and r_2 (r_1 = 1.5 r_2) through 1 K are in the ratio : Answer: 1. 27/8 Heat needed for a 1 K rise is Q=mcΔ T . Both spheres are copper, so c is the same and Q∝ m∝ r³ . Q₁/Q₂=(r₁/r₂)³=(1.5)³=27/8... Specific heat capacity, calorimetry, change of state, latent heat 1 answer
A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is : Answer: 3. 10.0 g Capillary rise: h=2Tcosθ/rρ g , so h∝1/r . Mass of water in the tube m=ρπ r²h∝ r²·1/r=r . Radius doubled gives mass double... Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise 1 answer
A small hole of area of cross-section 2 mm^2 is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s^2, the rate of flow of water through the open hole would be nearly : Answer: 1. 12.6×10⁻⁶ m ³ /s By Torricelli's theorem the speed of efflux is v=√(2gh) . v=√(2×10×2)=√(40)≈6.32 m/s. Rate of flow =Av=2×10⁻⁶×6.... Bernoulli's principle and applications 1 answer
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : (α_Cu = 1.7×10^-5 K^-1 and α_Al = 2.2×10^-5 K^-1) Answer: 4. 68 cm The difference in length stays the same at all temperatures only if both rods expand by the same amount: Δ l_Cu=Δ l_Al . l_... Heat, temperature and thermal expansion 1 answer
The unit of thermal conductivity is : Answer: 4. W m ⁻¹ K ⁻¹ From Q/T=KA Δθ/L , K=(Q/t) L/A Δθ . Unit of Q/t is W, L is m, A is m ² , Δθ is K. So K has unit W m/m² K=W m⁻¹K⁻¹ . Heat transfer: conduction, convection, radiation 1 answer
When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L+l). The elastic potential energy stored in the extended wire is : Answer: 3. 1/2Mgl The energy stored in a stretched wire equals the work done by the stretching force, which grows linearly from 0 to Mg . U=... Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli 1 answer
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5×10^-2 N/m. The pressure inside the bubble equals at a point Z_0 below the free surface of water in a container. Taking g = 10 m/s^2, density of w… Answer: 3. 1 cm A soap bubble has two surfaces, so the excess pressure inside is Δ P=4T/R . Δ P=dfrac4×2.5×10⁻²10⁻³=100\ Pa . At depth Z₀ in... Surface energy, surface tension, angle of contact, excess pressure, drops, bubbles, capillary rise 1 answer
Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δ l on applying a force F, how much force is… Answer: 1. 9 F Same volume: A l=3A l₂ , so the second wire has length l₂=l/3 . From Y=F l/A Δ l , F=YAΔ l/l . F₂=Y(3A)Δ l/l/3=9·YAΔ l/l=9F Elastic behaviour, stress-strain, Hooke's law, Young's, bulk and rigidity moduli 1 answer
The power radiated by a black body is P and it radiates maximum energy at wavelength, λ_0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 34λ_0, the power radiated by it becomes nP. The value of n… Answer: 2. 256/81 Wien's law: λ_mT= constant, so T∝dfrac1λ_m . Stefan's law: P∝ T⁴ . New wavelength is 3/4λ₀ , so T'=4/3T . n=(4/3)⁴=256/81 Heat transfer: conduction, convection, radiation 1 answer

Page 1 of 2