Properties of Matter

A metallic sphere cools from 50oC to 40o in 300 s. If atmospheric temperature around is 20oC,
then the sphere’s temperature after the next 5 minutes will be close to :

A cylindrical vessel containing a liquid is
rotated about its axis so that the liquid rises at
its sides as shown in the figure. The radius of
vessel is 5 cm and the angular speed of
rotation is \(\omega\) rad s–1. The difference in the
he...

A capillary tube made of glass of radius 0.15
mm is dipped vertically in a beaker filled with
methylene iodide (surface tension = 0.05 Nm–1,
density = 667 kg m–3) which rises to height h in
the tube. It is observed that the two tangents
dra...

A wire of density 9 \(\times\) 10–3 kg cm–3 is stretched
between two clamps 1 m apart. The resulting
strain in the wire is 4.9 \(\times\) 10–4. The lowest
frequency of the transverse vibrations in the
wire is : (Young’s modulus of wire ...

The top of a water tank is open to air and its water level is mainted. It is giving out 0.74 m3 water per minute through a circular opening of 2 cm radius in its wall. The depth of the center of the opening from the level of water in the ta...

If 'M' is the mass of water that rises in a capillary
tube of radius 'r', then mass of water which will
rise in a capillary tube of radius '2r' is :

A simple pendulum oscillating in air has period
T. The bob of the pendulum is completely
immersed in a non-viscous liquid. The density
of the liquid is
1/16 th of the material of the bob.
If the bob is inside liquid all the time, its period...

A wooden block floating in a bucket of water
has 4/5 of its volume submerged. When certain
amount of an oil is poured into the bucket, it
is found that the block is just under the oil
surface with half of its volume under water and
half in ...

A steel wire having a radius of 2.0 mm,
carrying a load of 4 kg, is hanging from a
ceiling. Given that g = 3.1 p ms–2, what will be
the tensile stress that would be developed in the
wire ?

Water from a pipe is coming at a rate of
100 litres per minute. If the radius of the pipe
is 5 cm, the Reynolds number for the flow is
of the order of : (density of water = 1000 kg/m3,
coefficient of viscosity of water = 1mPas)

A boy's catapult is made of rubber cord which
is 42 cm long, with 6 mm diameter of
cross-section and of negligible mass. The boy
keeps a stone weighing 0.02kg on it and
stretches the cord by 20 cm by applying a
constant force. When released...

Young's moduli of two wires A and B are in the
ratio 7 : 4. Wire A is 2 m long and has radius R.
Wire B is 1.5 m long and has radius 2 mm. If
the two wires stretch by the same length for a
given load, then the value of R is close to :-

A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus
experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The...

A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by :

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the ...

The number density of molecules of a gas depends on their distance r from the origin as, \(n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}\).
Then the total number of molecules is proportional to :

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of
Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net
longitudinal compressional force F, its...

A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous
fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these
spheres acquires a ...

A liquid of density \(\rho\) is coming out of a hose pipe of radius a with horizontal speed \(\upsilon\) and hits a mesh. 50% of
the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the sam...

Water flows into a large tank with flat bottom at the rate of 10–4m3s–1. Water is also leaking out of a hole ofarea 1 cm2 at its bottom. If the height of the water in the tank remains steady, then this height is -

The ratio of surface tensions of mercury and
water is given to be 7.5 while the ratio of thier
densities is 13.6. Their contact angles, with
glass, are close to 135° and 0°, respectively. It
is observed that mercury gets depressed by an
amo...

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum
weight that can be put on the block without fully submerging it under water? [Take, density of water = 103
kg/m3]

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support
a 400 N load without exceeding its elastic limit?

A submarine experiences a pressure of 5.05 × 106
Pa at a depth of d1 in a sea. When it goes further to a depth
of d2, it experiences a pressure of 8.08 × 106
Pa. Then d2 –d1 is approximately (density of water = 103
kg/m3
and acceleration...

In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm2
are used. The
wires are connected in series and one end of the combined wire is connected to a rigid support and other end
is subjected to elongati...

Water from a tap emerges vertically downwards with an initial speed of 1.0 ms–1
. The cross-sectional area of
the tap is 10–4 m2. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cros...

A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let P2 be the pressure inside the inner bubble and P0, the pressure outside the outer bubble. Radius of another bubble with pressure dif...

A thin uniform tube is bent into a circle of radius \(r\) in the vertical plane. Equal volumes of two immiscible liquids, whose densities are \({\rho _1}\) and \({\rho _2}\) \(\left( {{\rho _1} > {\rho _2}} \right),\) fill half the circle. ...

A body takes 10 minutes to cool from 60oC to 50oC. The tempertature of surroundings is constant at 25oC. Then, the temperature of the body after next 10 minutes will be approximately :

As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material i...

When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes \({{5r} \over 4}.\) Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (i...

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a
cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross
section of cylindrical contain...

Two tubes of radii r1 and r2, and lengths l1 and l2 , respectively, are connected in series
and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes.
If P2 is 4P1 and l...

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his
density remains same, the stress in the leg will change by a factor of :

A uniformly tapering conical wire is made from a material of Young’s modulus
Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wir...

Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water
coming down towards the gro...

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are sch...

A bottle has an opening of radius a and length b. A cork of length b and radius (a + \(\Delta\)a) where (\(\Delta\)a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coe...

A thin 1 m long rod has a radius of 5 mm. A force of 50 \(\pi\)kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the...

The pressure that has to be applied to the ends of a steel wire of length \(10\) \(cm\) to keep its length constant when its temperature is raised by \({100^ \circ }C\) is:
(For steel Young's modulus is $$2 \times {10^{11}}\,\,N{m^{ - 2}}$...

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities \({d_1}\) and \({d_2}\) are filled in the tube. Each liquid subtends \({90^ \circ }\) angle at center. Radius joining their interface makes an angle...

An open glass tube is immersed in mercury in such a way that a length of \(8\) \(cm\) extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional \(46\) \(cm\). What...

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius \(R\) and making a circular contact of radius \(r\) with the bottom \(R\) and making a circular contact of radius $...

If a piece of metal is heated to temperature \(\theta\) and then allowed to cool in a room which is at temperature \({\theta _0},\) the graph between the temperature \(T\) of the metal and time \(t\) will be closest to

A uniform cylinder of length \(L\) and mass \(M\) having cross-sectional area \(A\) is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density \(\sigma\) at equili...

A liquid in a beaker has temperature \(\theta \left( t \right)\) at time \(t\) and \({\theta _0}\) is temperature of surroundings, then according to Newton's law of cooling the correct graph between $${\log _e}\left( {\theta - {\theta _0}}...

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of \(1.5 \times {10^{ - 2}}\,\,N\) (see figure). The length of the slider is \(30\) \(cm\) and its weight negligible. The surface tension of the liquid ...

Work done in increasing the size of a soap bubble from a radius of \(3\) \(cm\) to \(5\) \(cm\) is nearly (Surface tension of soap solution \(= 0.03N{m^{ - 1}},\)

Water is flowing continuously from a tap having an internal diameter \(8 \times {10^{ - 3}}\,\,m.\) The water velocity as it leaves the tap is \(0.4\,\,m{s^{ - 1}}\) . The diameter of the water stream at a distance $$2 \times {10^{ - 1}}\,\...

A ball is made of a material of density \(\rho\) where \({\rho _{oil}}\, < \rho < {\rho _{water}}\) with \({\rho _{oil}}\) and \({\rho _{water}}\) representing the densities of oil and water, respectively. The oil and water are immiscible...