Mechanical Properties of Solids and Fluids
[ Given surface tension of water = 72 × 10–3 N/m and density of water = 103 kg/m3 ].
The Young’ s modulus of steel is twice that of brass. Two wires of the same length and same area of cross section, one of steel and another of brass, are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of
|Column I||Column II|
|(A)||(P)||The force acting on the particle is zero at x = a.|
|(B)||(Q)||The force acting on the particle is zero at x = 0.|
|(C)||(R)||The force acting on the particle is zero at x = −a|
|(D)||(S)||The particle experiences an attractive force towards x = 0 in the region |x| < a.|
|(T)||The particle with total energy can oscillation about the point x = −a.|
under its own gravity. If P(r) is the pressure at r (r < R), then the correct option(s) is(are)
(Pair = 1.2 kg/m3)
(g = gravitational acceleration)
connected by a massless string and placed in liquids L1 and L2 of densities σ1 and σ2 and
viscosities Ƞ1 and Ƞ2, respectively. They float in equilibrium with the sphere P in L1 and
sphere Q in L2 and the string being taut (see figure). If sphere P alone in L2 has terminal
velocity and Q alone in L1 has terminal velocity , then
(For steel, Young's modulus is 2 × 1011 Nm–2 and coefficient of thermal expansion is 1.1 × 10–5 K–1.)
(Atmospheric pressure = 76 cm of Hg)
(density of water is ρw)
If the piston is pushed at a speed of 5 mms−1, the air comes out of the nozzle with a speed of
If the density of air is and that of the liquid , then for a given piston, speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to
A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 103 kg/m3 and 2.2 × 1011 N/m2 respectively?
One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop of this to be possible? The surface tension is T, density of liquid is ρ and L is its latent heat of vaporization.
A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are)
Reason The moving liquid exerts equal and opposite force.
(i) gravitational force with time
(ii) viscous force with time
(iii) net force acting on the ball with time?
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
Reason Water works as glue and sticks two glass plates.
Reason Height through which liquid rise in capillary tube inversely proportional to the capillary tube.
The potential energy of particle in a force field is , where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is :
A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
Steel wire of length ‘L’ at 40 oC is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40 oC to 30 oC to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 10-5/oC, Young’s modulus of steel is 1011 Nm−2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly.
Reason : surface tension of liquid decreases with increase in temperature.
Reason : where symbols have their usual meaning.
Reason : During floating the body will experience net downward force in that case.
Two solid spheres A and B of equal volumes but of different densities are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius (assuming ) is
A 0.1kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 4.910-7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s-1. If the Young’s modulus of the material of the wires is , the value of n is
Reason Floating of ship in the water is not possible because of buoyancy force which is present due to pressure difference.
Two soup bubbles and are kept in a closed chamber where the air is maintained to pressure The radii of bubbles and are 2 cm and 4 cm, respectively, surface tension of the soap-water used to make bubbles is Find the ratio where and are the number of moles of air in bubbles and respectively. [Neglect the effect of gravity].
A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vesse becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice. [Take atmospheric pressure density of water and Neglect any effect of surface tension].
A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub − hemispherical soap bubble as shown in figure. Just after opening the valve.
(A) the cylinder will not move up and it will remain at its original position.
(B) for h2 = h/3, the cylinder again starts moving up
(C) for h2 = h/4, the cylinder again starts moving up
(D) for h2 = h/5, the cylinder again starts moving up
(B) Mg − Vρg
(C) Mg + πR2hρg
(D) ρg(V + πR2h)
(For the steel wire : Young’s modulus = 2.1 × 1011 Pa; density = 7860 kg/m3; specific heat = 420 J/kg-K)