## Numerical

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius $0.1 \mathrm{~mm}$ is dipped ...

A train with cross-sectional area St
is moving with speed vt
inside a long tunnel of cross-sectional
area S0 (S0 = 4St). Assume that almost all the ai...

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total
mass is 480 kg. Its effective volume giving the ...

A cubical solid aluminium (bulk modulus = $$ - V{{dP} \over {dV}} = 70GPa$$) block has an edge length of 1 m on the surface of the earth. It is kept o...

When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to
the surface tension of water. To calculate ...

A block of weight 100 N is suspended by copper and steel wires of same cross-sectional area 0.5 cm2 and length $$\sqrt 3 $$ m and 1 m, respectively. T...

A liquid at 30$$^\circ $$C is poured very slowly into a Calorimeter that is at temperature of 110$$^\circ $$C. The boiling temperature of the liquid i...

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $${T_1} = 300\,K$$ an...

A drop of liquid of radius $$R = {10^{ - 2}}\,m$$ having surface tension $$S = {{0.1} \over {4\pi }}N{m^{ - 1}}$$ divides itself into $$K$$ identical...

Consider two solid spheres P and Q each of density 8 gm cm–3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density...

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m$$^2$$. The radii of bubbles A and B are 2 cm and 4...

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 heigh...

## MCQ (More than One Correct Answer)

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma=$ $\frac{5}{3}$. The bubble is exposed to the at...

An ideal gas of density $\rho=0.2 \mathrm{~kg} \mathrm{~m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=$ $0.8 \mathrm{~kg} \mathrm{~s}...

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed incline...

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of
potassium permanganate (KMnO4) of different concentrat...

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0$$^\...

Consider a thin square plate floating on a viscous liquid in a large tank. The height $$h$$ of the liquid in the tank is much less than the width of t...

A uniform capillary tube of inner radius $$r$$ is dipped vertically into a beaker filled with water. The water rises to a height $$h$$ in the capillar...

A human body has a surface area of approximately $$1\,m{}^2.$$ The normal body temperature is $$10$$ $$K$$ above the surrounding room temperature $${T...

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r (r <...

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in...

Two spheres P and Q for equal radii have densities $$\rho$$1 and $$\rho$$2, respectively. The spheres are connected by a massless string and placed in...

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This h...

A solid sphere of radius R and density $$\rho $$ is attached to one end of a mass-less spring of force constant k.
The other end of the spring is conn...

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other en...

A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of ...

Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of densi...

## MCQ (Single Correct Answer)

An open-ended U-tube of uniform cross-sectional area contains water (density 103 kg m−3
). Initially the
water level stands at 0.29 m from the bottom ...

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It ...

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is
at rest, the water jet coming out of ...

A glass capillary tube is of the shape of truncated cone with an apex angle $$\alpha$$ so that its two ends have cross sections of different radii. Wh...

If the piston is pushed at a speed of 5 mm s$$-$$1, the air comes out of the nozzle with a speed of

If the density of air is $$\rho$$a and that of the liquid $$\rho$$l, then for a given piston speed the rate (volume per unit time) at which the liquid...

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...

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 ...

When liquid medicine of density $$\rho $$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pre...

When liquid medicine of density $$\rho $$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pre...

When liquid medicine of density $$\rho $$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the
top of the dropper is pre...

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...

STATEMENT - 1 :
The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends t...

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

When the gas bubble is at a height y from the bottom, its temperature is :

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

Water is filled up to a height $$h$$ in a beaker of radius $$R$$ as shown in the figure. The density of water is $$\rho$$, the surface tension of wate...

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the ...