List of top Physics Questions on Fluid Mechanics

A body of mass $m$ connected to a massless and unstretchable string goes in a vertical circle of radius $R$ under gravity $g$ . The other end of the string is fixed at the center of the circle. If velocity at the top of the circular path is $v = \sqrt{ngR}$ , where $n \geq 1$ , then the ratio of kinetic energy of the body at bottom to that at top of the circle is:

A tube of length L is shown in the figure. The radius of cross section at point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be:

A small rigid spherical ball of mass $M$ is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider $g$ as acceleration due to gravity):

Given below are two statements:
Statement-I: The hot water flows faster than cold water.
Statement-II: Soap water has higher surface tension as compared to fresh water.
In the light of the above statements, choose the correct answer from the options given below:

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$ . The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to:

A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

In the experiment for measurement of viscosity $\eta$ of a given liquid with a ball having radius $R$ , consider following statements: A. Graph between terminal velocity

V

and

R

will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of

\eta

will change.

Consider the following statements:
Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid. As the temperature of liquid rises, the coefficient of viscosity increases. As the temperature of gas increases, the coefficient of viscosity increases. The onset of turbulence is determined by Reynolds number. In a steady flow, two streamlines never intersect.
Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion $A$ and the other as Reason $R$ :
Assertion $A$ : A sound wave has higher speed in solids than in gases.
Reason $R$ : Gases have higher value of Bulk modulus than solids.

A bead of mass $m$ slides without friction on the wall of a vertical circular hoop of radius $R$ as shown in figure. The bead moves under the combined action of gravity and a massless spring $k$ attached to the bottom of the hoop. The equilibrium length of the spring is $R$ . If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes $R$ , would be (spring constant is $k$ , $g$ is acceleration due to gravity):

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-6} \, \text{C}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3} \, \text{N}$ . The distance between them is (Take $\frac{1}{4\pi \epsilon_0} = 9 \times 10^9$ in SI units):

The position vector of a moving body at any instant of time is given as r = ( 5t² $\hat{i}$ - 5t $\hat{j}$ ) m. The magnitude and direction of velocity at $t = 2 \, \text{s}$ are:

N equally spaced charges each of value $q$ are placed on a circle of radius $R$ . The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop $B$ encloses the whole circle, whereas a smaller Amperian loop $A$ encloses a small segment. The difference between enclosed currents, $I_B - I_A$ for the given Amperian loops is:

In photoelectric effect, the stopping potential $V_0$ vs frequency $\nu$ curve is plotted. $h$ is the Planck's constant and $\phi_0$ is the work function of metal.
(A) $V_0$ vs $\nu$ is linear.
(B) The slope of $V_0$ vs $\nu$ curve is $\frac{\phi_0}{h}$ .
(C) $h$ constant is related to the slope of $V_0$ vs $\nu$ line.
(D) The value of electric charge of electron is not required to determine $h$ using the $V_0$ vs $\nu$ curve.
(E) The work function can be estimated without knowing the value of $h$ .
Choose the correct answer from the options given below:

The energy $E$ and momentum $p$ of a moving body of mass $m$ are related by some equation. Given that $c$ represents the speed of light, identify the correct equation:

The fractional compression $\frac{\Delta V}{V}$ of water at the depth of 2.5 km below the sea level is:

A tube of length L is shown in the figure. The radius of cross section at point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be:

A small rigid spherical ball of mass $M$ is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider $g$ as acceleration due to gravity):

In photoelectric effect, the stopping potential $V_0$ vs frequency $\nu$ curve is plotted. $h$ is the Planck's constant and $\phi_0$ is the work function of metal.
(A) $V_0$ vs $\nu$ is linear.
(B) The slope of $V_0$ vs $\nu$ curve is $\frac{\phi_0}{h}$ .
(C) $h$ constant is related to the slope of $V_0$ vs $\nu$ line.
(D) The value of electric charge of electron is not required to determine $h$ using the $V_0$ vs $\nu$ curve.
(E) The work function can be estimated without knowing the value of $h$ . \text{Choose the correct answer from the options given below:}

N equally spaced charges each of value $q$ are placed on a circle of radius $R$ . The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop $B$ encloses the whole circle, whereas a smaller Amperian loop $A$ encloses a small segment. The difference between enclosed currents, $I_B - I_A$ for the given Amperian loops is:

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-6} \, \text{C}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3} \, \text{N}$ . The distance between them is (Take $\frac{1}{4\pi \epsilon_0} = 9 \times 10^9$ in SI units):

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.
Reason (R): A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation.
In light of the above statements, choose the most appropriate answer from the options given below:

An electric dipole of mass $m$ , charge $q$ , and length $l$ is placed in a uniform electric field $\mathbf{E} = E_0 \hat{i}$ . When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

Consider $I_1$ and $I_2$ are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If $L_1$ = self inductance of coil 1, $M_{12}$ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be:

The energy $E$ and momentum $p$ of a moving body of mass $m$ are related by some equation. Given that $c$ represents the speed of light, identify the correct equation: