Properties of Matter

Potential energy as a function of r is given by \(U = {A \over {{r^{10}}}} - {B \over {{r^5}}}\), where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 \(\times\) 108 Nm\(-\)2, Density of sea water = 103 kgm\(-\)3, g = 9.8 m/s2)

A uniform heavy rod of weight 10 kg ms\(-\)2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 \(\times\) 1011 Nm\(-\)2. Neglecting the lateral contraction, find th...

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 \(\times\) 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the com...

A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10\(-\)6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.(Young's modulus of rubber = 0.5 $$\time...

A body takes 4 min. to cool from 61\(^\circ\) C to 59\(^\circ\) C. If the temperature of the surroundings is 30\(^\circ\) C, the time taken by the body to cool from 51\(^\circ\) C to 49\(^\circ\) C is :

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact...

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging steam of water strikes the ground at the maximum r...

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop...

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 \(\times\) 10\(-\)5 m and density 1.2 \(\times\) 103 kgm\(-\)3 ? Take viscosity of liquid = 1.8 \(\times\) 10\(-\)5 Nsm\(-\)2. (Neglect buoya...

Wires W1 and W2 are made of same material having the breaking stress of 1.25 \(\times\) 109 N/m2. W1 and W2 have cross-sectional area of 8 \(\times\) 10\(-\)7 m2 and 4 \(\times\) 10\(-\)7 m2, respectively. Masses of 20 kg and 10 kg hang fro...

A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :

The normal density of a material is \(\rho\) and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .........

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7....

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \({{24} \over \pi } \times {10^2}\) Nm-2. What is the minimum radius of the wire ? (Take g = 10 ms-2)

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young's modulus is :

Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :

A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ___________ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the ...

If Y, K and \(\eta\) are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

In 5 minutes, a body cools from 75\(^\circ\)C to 65\(^\circ\)C at room temperature of 25\(^\circ\)C. The temperature of body at the end of next 5 minutes is _________\(^\circ\) C.

The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is :

Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is :

The length of a metal wire is l1, when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is :

A steel rod with y = 2.0 \(\times\) 1011 Nm\(-\)2 and \(\alpha\) = 10\(-\)5 \(^\circ\)C\(-\)1 of length 4 m and area of cross-section 10 cm2 is heated from 0\(^\circ\)C to 400\(^\circ\)C without being allowed to extend. The tension produced...

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The...

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m2. The tank has an opening B near the bottom whose cross-section area is 1 cm2. A load of 24 kg is applied on the water at the top when the height of the water ...

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm3 of oleic acid per cm3 of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm2 by consid...

An object is located at 2 km beneath the surface of the water. If the fractional compression \({{\Delta V} \over V}\) is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of wa...

The pressure acting on a submarine is 3 \(\times\) 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : (Assume that atmospheric pressure is 1 \(\times\) 105 Pa densi...

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10\(-\)3 Pa s, respectively. (Density of water : 103 kg/m3...

Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm–2
between A and B where the area of cross section
are 40 cm2 and 20 cm2, respectively. Find the
rate of flow of water through the tube.
(density of water...

Two steel wires having same length are
suspended from a ceiling under the same load.
If the ratio of their energy stored per unit
volume is 1 : 4, the ratio of their diameters is:

A small spherical droplet of density d is floating
exactly half immersed in a liquid of density \(\rho\)
and surface tension T. The radius of the droplet
is (take note that the surface tension applies an
upward force on the droplet) :

A leak proof cylinder of length 1m, made of
a metal which has very low coefficient of
expansion is floating vertically in water at 0°C
such that its height above the water surface is
20 cm. When the temperature of water is
increased to 4°C,...

Consider a solid sphere of radius R and mass
density \(\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right)\) , \(0 < r \le R\) The
minimum density of a liquid in which it will
float is :

Two liquids of densities \({\rho _1}\) an \({\rho _2}\) (\({\rho _2}\) = 2\({\rho _1}\)) are
filled up behind a square wall of side 10 m as
shown in figure. Each liquid has a height of
5 m. The ratio of the forces due to these liquids
exert...

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and
minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum
and the maximum velocities of fluid in this pipe is :

An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its
frequency of oscillation along the vertical direc...

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms–1 at a point
where the pressure is P pascal. At another point where pressure is \({P \over 2}\)
Pascal its speed is V ms–1. If
the density of the fluid ...

A hollow spherical shell at outer radius R floats
just submerged under the water surface. The
inner radius of the shell is r. If the specific
gravity of the shell material is \({{27} \over 8}\) w.r.t water,
the value of r is :

In an experiment to verify Stokes law, a small
spherical ball of radius r and density \(\rho\) falls
under gravity through a distance h in air before
entering a tank of water. If the terminal velocity
of the ball inside water is same as it...

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s–2. The density of water is
1 gm cm–3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980
cm/s2).

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density
d. The area of the base of both vessels is S but the height of liquid in one vessel is x1
and in the
other, x2
. When both cylinders are c...

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the
length of the side of the cube is close to :
(Given bulk modulus of metal, B = 8 \(\times\) 1010 Pa)

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their
volumes is :

When a long glass capillary tube of radius
0.015 cm is dipped in a liquid, the liquid rises
to a height of 15 cm within it. If the contact angle
between the liquid and glass to close to 0o, the
surface tension of the liquid, in milliNewton ...