CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 11 - MCQExams.com

For which of the following does the centre of mass lie outside the body?
  • A pencil
  • A shot put
  • A dice
  • A bangle
A metallic sphere having mass $$2 \,kg$$ is moving with a velocity of $$10 \,m /s.$$ The momentum of the sphere in kg metre / sec. will be-
  • $$1 / 5$$
  • $$5$$
  • $$12$$
  • $$20$$
In kinetic theory of gases , a molecule of mass $$m$$ of an ideal gas collides with a wall of  vessel with velocity $$V$$. The change in the linear momentum of the molecule is 
  • $$2 \,mV$$
  • $$mV$$
  • $$-mV$$
  • Zero
The total momentum of the molecules of $$1\,gm\, mol $$of a gas in a container at rest of $$300\,K $$ is 
  • $$2 \times \sqrt{3 R \times 300} \, gm \times cm / sec $$
  • $$2 \times 3 \times R \times 300 \, gm \times cm / sec $$
  • $$1 \times \sqrt{3 \times R \times 300} \, gm \times cm / sec $$
  • Zero
A $$57.0-g$$ tennis ball is traveling straight at a player at $$21.0\ m/s$$. The player volleys the ball straight back at $$25.0\ m/s$$. If the ball remains in contact with the racket for $$0.060\ 0\ s$$, what average force acts on the ball?
  • $$22.6\ N$$
  • $$32.5\ N$$
  • $$43.7\ N$$
  • $$72.1\ N$$
  • $$102\ N$$
The ratio of the radii of gyration of a circular
disc to that of a circular ring, each of same mass
and the radius around their respective axes is -

  • $$\dfrac {\sqrt2}{1}$$
  • $$\dfrac{\sqrt2}{\sqrt3}$$
  • $$\dfrac{\sqrt3}{\sqrt2}$$
  • $$\dfrac{1}{\sqrt{2}}$$
Four thin metal rods, each of mass $$M$$ and length $$L$$, are welded to form a square. The moment of inertia of the composite structure about a line which bisects any two opposite rods is:
  • $$\dfrac{ML^{2}}{6}$$
  • $$\dfrac{ML^{2}}{3}$$
  • $$\dfrac{ML^{2}}{2}$$
  • $$\dfrac{2ML^{2}}{3}$$
Three identical spheres each of mass m and radius R are placed touching each other so that their centres A, B and C lie on a straight line. The position of their centre of mass from the centre of A is
  • $$\displaystyle \frac{2R}{3}$$
  • 2R
  • $$\displaystyle \frac{5R}{3}$$
  • $$\displaystyle \frac{4R}{3}$$
An automobile is started from rest with one of its doors initially at right angles. lf the hinges of the door are toward the front of the car, the door will shut as the automobile picks up speed.  The acceleration a is constant and the centre of mass is at a distance d from the hinges. The time $$T$$ needed for the doors to close is given by:
 $$\left [ Given:\displaystyle\int_{0}^{\frac{\pi }{2}}\dfrac{d\theta }{\sqrt{sin\theta }}=N \right ]$$(Consider the door as a square plate)
  • $$\mathrm{T}=(\sqrt{\dfrac{3\mathrm{d}}{2\mathrm{a}}}) \mathrm{N}$$
  • $$\mathrm{T}=(\sqrt{\dfrac{\mathrm{d}}{3\mathrm{a}}}) \mathrm{N}$$
  • $$\mathrm{T}=(\sqrt{\dfrac{2\mathrm{d}}{\mathrm{a}}}) \mathrm{N}$$
  • $$\mathrm{T}=(\sqrt{\dfrac{2\mathrm{d}}{3\mathrm{a}}}) \mathrm{N}$$
A uniform sheet each of thickness 10 units is
cut into the shape as shown. Compute then x
and y-coordinates of the centre of mass of the
piece from point A.


40056.jpg
  • 17.5, 22.5
  • 22.5, 17.5
  • 10.5, 22.5
  • 190/7, 125/7
Three identical thin rods each of mass $$m$$ and length $$L$$ are joined together to form an equilateral triangular frame. The moment of inertia of frame about an axis perpendicular to the plane of frame and passing through a corner is:
  • $$\dfrac{2mL^{2}}{3}$$
  • $$\dfrac{3mL^{2}}{2}$$
  • $$\dfrac{4mL^{2}}{3}$$
  • $$\dfrac{3mL^{2}}{4}$$
A thin uniform metallic triangular sheet of mass M has sides $$AB=BC=L$$. Its moment of inertia about the axis AC lying in the plane of the sheet is:
  • $$\dfrac{ML^{2} }{12}$$
  • $$\dfrac{ML^{2} }{6}$$
  • $$\dfrac{ML^{2} }{3}$$
  • $$\dfrac{2ML^{2} }{3}$$

In the system shown, a force of $$100$$ N is applied at the end shown. What is the magnitude $$\tau $$ (in N-m) of the torque which was produced on the drum for starting motion? (Given that the coefficient of static friction is $$0.1$$)

43888_53091f668eac49339f30b9ab41cb6758.png
  • $$10$$
  • $$5$$
  • $$20$$
  • $$25$$
A car (open at the top) of mass 9.75 kg is coasting along a level track at 1.36 m/s, when it begins to rain hard. The raindrops fall vertically with respect to the ground. When it has collected 0.5 kg of rain, the speed of the car is
  • 0.68 m/s
  • 1.29 m/s
  • 2.48 m/s
  • 9.8 m/s
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $$0_0$$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is :
  • $$0_0 + \dfrac{ML^2}{2}$$
  • $$0_0 + \dfrac{ML^2}{4}$$
  • $$0_0 + 2ML^2$$
  • $$0_0 + ML^2$$
Find the momentum of each particle.
  • $$p=2\mu\sqrt{v_1^2+v_2^2}$$
  • $$p=\mu\sqrt{v_1^2+v_2^2}$$
  • $$p=3\mu\sqrt{v_1^2+v_2^2}$$
  • $$p=4\mu\sqrt{v_1^2+v_2^2}$$
The arrangement shown in figure above consists of two identical uniform solid cylinders, each of mass $$m$$, on which two light threads are wound symmetrically. The friction in the axle of the upper cylinder is assumed to be absent. If the tension of each thread in the process of motion is $$\displaystyle T=\frac{mg}{x}$$, then the value of $$x$$ is :
141781_1d131792f4d44093ad03cb77c8f8f3c6.png
  • $$10$$
  • $$20$$
  • $$15$$
  • $$5$$
A train of mass $$M$$ is moving on a circular track of radius $$R$$ with a constant speed $$v$$. The length of the train is half of the perimeter of the track. The linear momentum of the train will be
  • $$zero$$
  • $$\dfrac {2Mv}{\pi}$$
  • $$MvR$$
  • $$Mv$$
The figure shows a uniform rod lying along the x-axis. The locus of all the points lying on the x-y plane, about which the moment of inertia of the rod is same as that about O, is:

120011_73ca36d6b06e4483b1e6e359918cd4e0.png
  • an ellipse
  • a circle
  • a parabola
  • a straight line
A chain $$AB$$ of mass $$m$$ and length $$L$$ is hanging on a smooth horizontal table as shown in the figure. If it is released from the position shown then the displacement of centre of mass of chain in magnitude, when end $$A$$  moves a distance $$\dfrac{L}{2}\ is\ X\sqrt{2}m $$.
Find $$X$$. ($$L = 32\  m$$)
131023_2bf284a508024e318108610a0e137ce4.png
  • $$8$$
  • $$9$$
  • $$10$$
  • $$16$$
Two identical bricks of length $$L$$ are piled one on top of the other on a table as shown in the figure. The maximum distance $$S$$ the top brick can overhang the table with the system still balanced is :
126851_74a27a999aed43f082ee0de7809efc98.png
  • $$ \dfrac{1}{2}L $$
  • $$ \dfrac{2}{3}L $$
  • $$ \dfrac{3}{4}L $$
  • $$ \dfrac{7}{8}L $$
Three point like equal masses $$m_1, m_2$$ and $$m_3$$ are connected to the ends of a mass-less rod of length $$L$$ which lies at rest on a smooth horizontal plane. At $$t = 0$$, an explosion occurs between $$m_2$$ and $$m_3$$, and as a result, mass $$m_3$$ is detached from the rod, and moves with a known velocity $$v$$ at an angle of $$30^o$$ with the y-axis. Assume that the masses $$m_2$$ and $$m_3$$ are unchanged during the explosion.
What is the velocity of the centre of mass of the system consisting of three masses after the expulsion?
161398_e9ab16d17cc848e8893cd4fff49769b9.PNG
  • $$\displaystyle \dfrac{v}{4} (\widehat i - 3 \widehat j)$$
  • $$\displaystyle \dfrac{v}{4} (- \widehat i + \sqrt{3} \widehat j)$$
  • $$-v$$
  • none of the above
Two wheels $$A$$ and $$B$$ are released from rest from points $$X$$ and $$Y$$ respectively on an inclined plane as shown in figure. Which of the following statement(s) is/are incorrect?

160698_54589c04f7b5468bbe0056143d5daddc.png
  • Wheel $$B$$ takes twice as much time to roll from $$Y$$ to $$Z$$ than that of wheel $$A$$ from $$X$$ to $$Z$$.
  • At point $$Z$$ velocity of wheel $$A$$ is four times that of wheel $$B$$
  • Acceleration of the wheel $$A$$ is four times that of wheel $$B$$
  • Both wheel take same time to arrive at point $$Z$$.
A particle of mass $$'m'$$ is rigidly attached at $$'A'$$ to a ring of mass $$'3m'$$ and radius $$'r.'$$ The system is released from rest and rolls without sliding. The angular acceleration of ring just after release is

160151_2ff833e9f13a415fa92a2952f11af471.png
  • $$\cfrac{g}{4r}$$
  • $$\cfrac{g}{6r}$$
  • $$\cfrac{g}{8r}$$
  • $$\cfrac{g}{2r}$$
Three particles of masses 1 kg, 2 kg and 3 kg are situated at the corners of the equilateral triangle move at speed 6 ms$$^{-1}$$, 3 ms$$^{-1}$$ and 2 ms$$^{-1}$$ respectively. Each particle maintains a direction towards the particle at the next corner symmetrically. Find velocity of COM of the system at this instant :
  • $$3 ms^{-1}$$
  • $$5 ms^{-1}$$
  • $$6 ms^{-1}$$
  • $$zero$$
Four identical rods are joined end to end to form a square. The mass of each rod is $$M$$. The moment of inertia of the square about the median line is 
  • $$\dfrac{Ml^{2}}{3}$$
  • $$\dfrac{Ml^{2}}{4}$$
  • $$\dfrac{Ml^{2}}{6}$$
  • none of these
A steel plate of thickness $$h$$ has the shape of a square whose side equals $$l$$, with $$h\ll l$$. The plate is rigidly fixed to a vertical axle $$OO$$ which is rotated with a constant angular acceleration $$\beta$$ (figure shown above). Find the deflection $$\lambda$$ assuming the sagging to be small.
156446_4e9d50f878fb45a4837c1bceff0d09db.png
  • $$\displaystyle\lambda=\frac{9\rho\beta l^5}{5Eh^2}$$
  • $$\displaystyle\lambda=\frac{7\rho\beta l^5}{3Eh^2}$$
  • $$\displaystyle\lambda=\frac{7\rho\beta l^5}{5Eh^2}$$
  • None of these
A particle of mass m comes down on a smooth inclined plane from point B at a height of h from rest. The magnitude of change in momentum of the particle between position A (just before arriving on horizontal surface) and C (assuming the angle of inclination of the plane as $$\theta$$ with respect to the horizontal) is :
  • 0
  • $$2m \sqrt{(2gh)} sin \theta$$
  • $$2m \sqrt{2gh} sin \displaystyle \left ( \frac{\theta}{2} \right )$$
  • $$2m \sqrt{(2gh)}$$

The radius of gyration of a plane lamina of mass $$M$$, length $$L$$ and breadth $$B$$ about an axis passing through its center of gravity and perpendicular to its plane will be

  • $$\displaystyle{\sqrt{\dfrac{(L^2+B^2)}{12}}}$$
  • $$\displaystyle{\sqrt{\dfrac{(L^2+B^2)}{8}}}$$
  • $$\displaystyle{\sqrt{\dfrac{(L^2+B^2)}{2}}}$$
  • $$\displaystyle{\sqrt{\dfrac{(L^3+B^3)}{12}}}$$
(i) Centre of gravity (C.G.) of a body is the point at which the weight of the body acts
(ii) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
(iii) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G.
(iv) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis
Which one of the following pairs of statements is correct ?
  • (iv) and (i)
  • (i) and (ii)
  • (ii) and (iii)
  • (iii) and (iv)
Two particles of equal mass have initial velocities $$2\hat{i}\, ms^{-1}\, and\, 2\hat{j}\, ms^{-1}$$. First particle has a constant acceleration $$(\hat{i}\,+\,\hat{j})\, ms^{-1}$$ while the acceleration of the second particle is always zero. The centre of mass of the two particles moves in :
  • Circle
  • Parabola
  • Ellipse
  • Straight line
Three rings each of mass m and radius r are so placed that they touch each other. The radius or gyration of the system about the axis as shown in the figure is:
295614_788ecdbc492a4222acdafa406acff545.png
  • $$\displaystyle \sqrt{\frac{6}{5}}r$$
  • $$\displaystyle \sqrt{\frac{5}{6}}r$$
  • $$\displaystyle \sqrt{\frac{6}{7}}r$$
  • $$\displaystyle \sqrt{\frac{7}{6}}r$$
Consider the following two statement-
[A] Linear momentum of a system of particle is zero
[B] kinetic energy of a system of particles is zero. Then
  • A does not imply B but B implies A
  • A implies B and B implies A
  • A does not imply B & B does not imply A
  • A implies B but B does not imply A
Linear mass density of the two rods system, $$AC$$ and $$CB$$ is $$x$$. Moment of inertia of two rods about an axis passing through $$AB$$ is

217285.jpg
  • $$\displaystyle \frac{xl^{3}}{4\sqrt{3}}$$
  • $$\displaystyle \frac{xl^{3}}{\sqrt{3}}$$
  • $$\displaystyle \frac{xl^{3}}{4}$$
  • $$\displaystyle \frac{xl^{3}}{6\sqrt{2}}$$
The moment of inertia of the plate about z-axis is
207597_8da2909e2deb447cbc71b0a672400412.png
  • $$\displaystyle\frac{ML^2}{12}$$
  • $$\displaystyle\frac{ML^2}{24}$$
  • $$\displaystyle\frac{ML^2}{6}$$
  • None of these
In the diagram shown below all three rods are of equal length L and equal mass M. The system is rotated such that rod B is the axis. What is the moment of inertia of the system?
430223.png
  • $$\dfrac {ML^{2}}{6}$$
  • $$\dfrac {4}{3} ML^{2}$$
  • $$\dfrac {ML^{2}}{3}$$
  • $$\dfrac {2}{3} ML^{2}$$
There are two particles of same mass. If one of the particles is at rest always and the other has an acceleration $$\bar{a}$$. Acceleration of center of mass is :
  • zero
  • $$\displaystyle\frac{1}{2}\, \bar{a}$$
  • $$\bar{a}$$
  • centre of mass for such a system can not be defined.
Fill in the blanks.
The effect of rotation of the earth is ......... at the equator and .............. at the poles. If the earth stops rotating. the weight of a body would .......... due to the absence of .............. force.
  • Minimum, maximum, decreases, gravitional
  • Maximum, minimum, increases, centrifugal
  • Maximum, minimum, decreases, centrifugal
  • Minimum, maximum, increases, gravitional
If torques of equal magnitudes are applied to a hollow cylinder and a solid sphere both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry and the sphere is free to rotate about an axis passing through its center. Which of the two will acquire a greater angular speed after a given time?
  • $${ \omega }_{ 1 } > { \omega }_{ 2 }$$
  • $${ \omega }_{ 1 } = { \omega }_{ 2 }$$
  • $${ \omega }_{ 2 } > { \omega }_{ 1 }$$
  • None of these
A cord of negligible mass is wound round the rim of fly wheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord as shown in the figure. The fly wheel is mounted on a horizontal axle with frictionless bearings. Compute the angular acceleration of the wheel.  
549472.png
  • $$8.25 kgm^2$$
  • $$6.25 kgm^2$$
  • $$4.8 kgm^2$$
  • $$1.0 kgm^2$$
A bar magnet of moment of inertia $$I$$ is vibrated in a magnetic field of induction $$\displaystyle 0.4\times { 10 }^{ -4 }T$$. The time period of vibration is $$12\  s$$. The magnetic moment of the magnet is $$\displaystyle 120\ { Am }^{ 2 }$$. The moment of inertia of the magnet is (in $$\displaystyle kg{ m }^{ 2 }$$) approximately:
  • $$\displaystyle 2.1{ \pi }^{ 2 }\times{ 10 }^{ -2 }$$
  • $$\displaystyle 1.57\times { 10 }^{ -2 }$$
  • $$\displaystyle 1728\times { 10 }^{ -2 }$$
  • $$\displaystyle 172.8\times { 10 }^{ -4 }$$
A wheel of radius $$r$$ and moment of inertia $$I$$ about its axis is fixed at the top of an inclined plane of inclination $$ \theta $$ as shown in the figure. A string is wrapped round the wheel and its free end supports a block of mass $$M$$ which can slide on the plane. Initially, the wheel is rotating at a speed of $$\omega$$ in a direction such that the block slides up the plane. How far will the block move before stopping?
545653.png
  • $$\dfrac{(I+ Mr^3) {\omega}^2}{4 Mg \sin \theta}$$
  • $$\dfrac{(I+ Mr^2) {\omega}^2}{2 Mg \sin \theta}$$
  • $$\dfrac{(I+ Mr^2) {\omega}^2}{5 Mg \sin \theta}$$
  • $$\dfrac{(I+ Mr^2) {\omega}^2}{7 Mg \sin \theta}$$
A rod is hinged at centre and rotated by applying the torque starting from rest ,the power developed by the torque with respect to time is of
  • cubic nature
  • quadratic nature
  • linear nature
  • sinusoidal nature
A particle of mass $$m$$ is subjected to an attractive central force of magnitude $$k/r^2$$, $$k$$ being a constant. If at the instant when the particle is at an extreme position in its closed orbit, at a distance $$a$$ from the centre of force, its speed is $$(k/2ma)$$, if the distance of other extreme position is $$b$$. Find $$a/b.$$
  • 4
  • 3
  • 5
  • 6
Find the moment of inertia of the rod AC about an axis BD as shown in figure. Mass of the rod is m and length is L

1002626_7edae635928b493db621072bcdd2801b.png
  • $$\dfrac{3mL^2 sin^2 \alpha}{2}$$
  • $$\dfrac{mL^2 sin^2 \alpha}{3}$$
  • $$\dfrac{3mL^2 sin^2 \alpha}{4}$$
  • $$\dfrac{3mL^2 sin^2 \alpha}{5}$$
A hoop of mass $$m$$ is projected on a floor with linear velocity $$v_{0}$$ and reverse spin $$\omega_{0}$$. The coefficient of friction between the hoop and the ground is $$\mu$$.
a. Under what condition will the hoop return back?
b. How far will it go?
c. How long will it continue to slip when its centre of mass becomes stationary?
d. What is the velocity of return?
  • a. $$\omega_{0} > \dfrac {v_{0}}{R}$$.
    b. $$\dfrac {v_{0}^{2}}{R}$$,
    c. $$\dfrac {R}{3\mu_{g}}\left (\omega_{0} - \dfrac {v_{0}}{R}\right )$$,
    d. $$\dfrac {\omega_{0}R}{2} - \dfrac {v_{0}}{2}$$.
  • a. $$\omega_{0} > \dfrac {v_{0}}{R}$$.
    b. $$\dfrac {v_{0}^{3}}{R}$$,
    c. $$\dfrac {R}{2\mu_{g}}\left (\omega_{0} - \dfrac {v_{0}}{R}\right )$$,
    d. $$\dfrac {\omega_{0}R}{4} - \dfrac {v_{0}}{2}$$.
  • a. $$\omega_{0} > \dfrac {v_{0}}{R}$$.
    b. $$\dfrac {v_{0}^{2}}{R}$$,
    c. $$\dfrac {R}{2\mu_{g}}\left (\omega_{0} - \dfrac {v_{0}}{R}\right )$$,
    d. $$\dfrac {\omega_{0}R}{3} - \dfrac {v_{0}}{2}$$.
  • a. $$\omega_{0} > \dfrac {v_{0}}{R}$$.
    b. $$\dfrac {v_{0}^{2}}{R}$$,
    c. $$\dfrac {R}{2\mu_{g}}\left (\omega_{0} - \dfrac {v_{0}}{R}\right )$$,
    d. $$\dfrac {\omega_{0}R}{2} - \dfrac {v_{0}}{2}$$.
Three identical rods, each of mass $$m$$ and length $$l$$, form an equilateral triangle. Moment of inertia about one of the sides is
984297_110fccd8007d49db85a6725a9fe139a2.png
  • $$\cfrac { m{ l }^{ 2 } }{ 6 } $$
  • $$m{ l }^{ 2 }\quad $$
  • $$\cfrac { 3m{ l }^{ 2 } }{ 4 } $$
  • $$\cfrac { 2m{ l }^{ 2 } }{ 3 } $$
Figure below shows the variation of the moment of inertia of a uniform rod about an axis normal to its length with the distance of the axis from the end of the rod. The moment of inertia of the rod about an axis passing through its centre and perpendicular to the its length is then
992794_579a4c13327940c9bcda89ea46485302.JPG
  • $$0.5 kg-m^2$$
  • $$0.15 kg-m^2$$
  • $$0.10 kg-m^2$$
  • $$0.05 kg-m^2$$
A plot of angular momentum of a rigid body (along y axis) about an axis with time (along x axis) gives rise to a straight line, whose equation is given by y = 3x+Find the torque acting on the body
  • 8 N-m
  • 3 N-m
  • 30 N-m
  • 0.3 N-m
A square frame ABCD is formed by four identical rods each of mass 'm' and length 'T'. This frame is in X - Y plane such that side AB coincides with X - axis and side AD along Y - axis. The moment of inertia of the frame about X - axis is
  • $$\dfrac{5ml^2}{3}$$
  • $$\dfrac{2ml^2}{3}$$
  • $$\dfrac{4ml^2}{3}$$
  • $$\dfrac{ml^2}{12}$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Physics Quiz Questions and Answers