CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 6 - MCQExams.com

All discs irrespective of their mass and radius move with same acceleration along an incline.
  • True
  • False
A ring of mass m and radius r rolls on an inclined plane. A torque is produced in the ring due to
  • $$mg sin \theta$$ and the radius of the ring
  • the perpendicular distance between the force and the point of contact and the force $$mg$$ acting on it
  • the perpendicular distance between the force and the point of contact and the normal force acting on the object
  • the perpendicular distance between the force and the point of contact and the force $$mg sin \theta$$ acting on it
A vertical rod AC, with C at ground and A being the top most point is moving in such a way, that A moves with a speed of 8 m/s, mid point of the rod B moves with a speed of 4 m/s. along the same direction, with what velocity will the point C move
  • 4 m/s
  • 8 m/s
  • 0 m/s
  • 1 m/s
The angular momentum of a particle rotating with an angular velocity $$\omega$$ distant r from a given origin is I. If the origin is shifted by 2r, then the new angular momentum of the particle with same angular velocity will be 
  • 2I
  • 9I
  • 4I
  • 3I
Statement related to center of gravity that is incorrect is
  • The center of gravity of an object is defined as the point through which its whole weight appears to act.
  • The center of gravity is sometimes confused with the center of mass.
  • The center of gravity always lies inside the object.
  • For an object placed in a uniform gravitational field, the center of gravity coincides with the center of mass.
In the image shown . AC is a rigid rod of length 12 cms rotating about point P, whose velocities are shown in the figure. Find the distance PC = x
1003151_80cd501d0f704fa3b16747abbac1e046.PNG
  • 12 cms
  • 8 cms
  • 4 cms
  • 2 cms
Which of the below statement is correct
  • All points in an object move in a straight line in rectilinear motion, while moves in a curved path when rotated about a fixed point
  • All points in an object move with the same linear speed when rotated about a fixed point
  • All points in an object move in a straight line, while the object moves in a curved path pivoted about a fixed point
  • All points in an object moves in a curved path, while the object is moving along a straight line
A disc rolling down the incline has lesser acceleration as compared to the same disc sliding down the incline
  • True
  • False
Only rotating bodies can have angular momentum.
  • True
  • False
Moment of inertia of a thin rod of mass $$m$$ and length $$l$$ about at axis passing though a point $$l/4$$ from one and perpendicular to the rod is:
  •  $$\frac { { ml }^{ 2 } }{ 12 }$$ 
  •  $$\frac { { ml }^{ 2 } }{ 13 }$$
  • $$\frac { { 7ml }^{ 2 } }{ 48 }$$
  •  $$\frac { { ml }^{ 2 } }{ 9 }$$
A constant torque is applied to a rigid body, whose moment of inertia is $$4 kg-m^2$$ around the axis of rotation. If the wheel starts from rest and attains an angular velocity of 20 rad/s in 10 s, what is the applied torque
  • $$18 N-m$$
  • $$8 N-m$$
  • $$4 N-m$$
  • $$6 N-m$$
Three objects of same mass but different geometries, capable of rotating have radius of gyration as 0.2, 0.5 and 0.A torque is applied to these objects when they are rotating with constant angular velocity. Which object will have a larger response time for showing the change in their angular velocity
  • Object with a radius of gyration of 0.7 will take a long time to respond to the torque
  • Object with a radius of gyration of 0.5 will take a long time to respond to the torque
  • Object with a radius of gyration of 0.2 will take a long time to respond to the torque
  • All objects with have same response time
A ball moving with a momentum of $$5kgm/s$$ strikes against a wall at an angle of $${45}^{o}$$ and is reflected at the same angle. The change in momentum will be (kg-m/s) :
1014413_68b7279ced6447559874e998ed0ee29f.PNG
  • $$7.07$$
  • $$14.14$$
  • $$8.00$$
  • $$7.5$$
Two blocks of masses $$10\ kg$$ and $$4\ kg$$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $$14\ m/s$$ to the heavier block in the direction of the lighter block, The velocity of the centre of mass is:
  • $$30\ m/s$$
  • $$20\ m/s$$
  • $$10\ m/s$$
  • $$5\ m/s$$
A jar filled with two non mixing liquids $$1$$ and $$2$$ having densities $$\rho_{1}$$ and $$\rho_{2}$$ respectively. A solid ball, made of a material of density $$\rho_{3}$$, is dropped in the jar. It comes to equilibrium in the position shown in the figure
1011944_05afe8def3bf4c51840271502d4ba3bb.png
  • $$\rho_{3} < \rho_{1} < \rho_{2}$$
  • $$\rho_{1} < \rho_{3} < \rho_{2}$$
  • $$\rho_{1} < \rho_{2} < \rho_{3}$$
  • $$\rho_{3} < \rho_{2} < \rho_{1}$$
Using the parallel axes theorem, find the $$M.l.$$ of a sphere of mass $$m$$ about an axis that touches it tangentially. Give that $$I_{cm}=\dfrac {2}{5}mr^{2}$$.
  • $$\dfrac {7}{5}\ mr^{2}$$
  • $$\dfrac {7}{15}\ mr^{2}$$
  • $$\dfrac {8}{15}\ mr^{2}$$
  • $$\dfrac {9}{15}\ mr^{2}$$
Find the angular momentum of a particle of mass $$m$$ describing a circle of radius $$r$$ with angular speed $$\omega$$.
  • $$2m{ \omega  }r^{ 2 }$$.
  • $$m{ \omega  }r^{ 2 }$$.
  • $$3m{ \omega  }r^{ 2 }$$.
  • $$4m{ \omega  }r^{ 2 }$$.
A wheel having moment of inertia $$4\ kg\ {m}^{2}$$ about its symmetrical axis, rotates at rate of $$240$$ rpm about it. The torque which can stop the rotation of the wheel in one minute is:
  • $$\dfrac {5\pi}{7}Nm$$
  • $$\dfrac {8\pi}{15}Nm$$
  • $$\dfrac {2\pi}{9}Nm$$
  • $$\dfrac {3\pi}{7}Nm$$
The linear momentum $$P$$ of a particle varies with time as follow $$P=a+{bt}^{2}$$. Where $$a$$ and $$b$$ are constants. The net force acting on the particle is:
  • Proportional to $$t$$
  • Proportional to $${t}^{2}$$
  • Zero
  • Constant
A block of mass $$2\ kg$$ is moving with a velocity of $$2\hat { i } -\hat { j } +3\hat { k }\ m/s$$. Find the magnitude and direction of momentum of the block with the $$x-$$axis.
  • $$2\sqrt {14}\ kg\ m/s$$,  $$\tan ^{ -1 }{ \left( \sqrt { \dfrac { 5 }{ 7 }  }  \right)  } $$ 
  • $$2\sqrt {7}\ kg\ m/s$$,  $$\tan ^{ -1 }{ \left( \sqrt { \dfrac { 2 }{ 7 }  }  \right)  } $$ 
  • $$2\sqrt {14}\ kg\ m/s$$,  $$\tan ^{ -1 }{ \left( \sqrt { \dfrac { 2 }{ 7 }  }  \right)  } $$ 
  • $$2\sqrt {9}\ kg\ m/s$$,  $$\tan ^{ -1 }{ \left( \sqrt { \dfrac { 3 }{ 7 }  }  \right)  } $$ 
The density of rod $$AB$$ increases linearly from $$A$$ to $$B$$. Its midpoint is $$O$$ and its centre of mass is at $$C$$. Four axes pass through $$A, B, O$$ and $$C$$, all perpendicular to the length of the rod. The moments of inertia of the rod about these axes are $${I}_{A}$$, $${I}_{B}$$,$${I}_{C}$$ respectively.
  • $${I}_{A}>{I}_{B}$$
  • $${I}_{A}<{I}_{B}$$
  • $${I}_{B}>{I}_{C}$$
  • $${I}_{O}<{I}_{C}$$
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 $$I_{0}$$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is :
  • $$I_{0}+ML^{2}/2$$
  • $$I_{0}+ML^{2}/4$$
  • $$I_{0}+2ML^{2}$$
  • $$I_{0}+ML^{2}$$
The $$M.I.$$ of a thin rod of length $$\ell$$ about the perpendicular axis through its centre is $$I$$. The $$M.I.$$ of the square structure made by four such rods about a perpendicular axis to the plane and through the centre will be :
  • $$4\ I$$
  • $$8\ I$$
  • $$12\ I$$
  • $$16\ I$$
A disc rolls down a plane of length $$L$$ and inclined at angle q, without slipping. its velocity on reaching the bottom will be :-
  • $$\sqrt{\dfrac{4gL \sin \theta}{3}}$$
  • $$\sqrt{\dfrac{2gL \sin \theta}{3}}$$
  • $$\sqrt{\dfrac{10gL \sin \theta}{7}}$$
  • $$\sqrt{4gL \sin \theta}$$
A rubber ball of mass $$10 gm$$ and volume $$15 cm^3$$ dipped in water to a depth of $$10 m$$. Assuming density of water uniform throughout the depth, find
(a) the acceleration of the ball, and
(b) the time taken by it to the surface if it is released from rest. take $$g = 980 cm/s^2$$.
  • (a) $$5.9 m/s^2$$     (b) $$2.02$$sec.
  • (a) $$4.9 m/s^2$$     (b) $$2.02$$sec.
  • (a) $$4.9 m/s^2$$     (b) $$12.02$$sec.
  • (a) $$8.9 m/s^2$$     (b) $$2.02$$sec.
A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations will be :-
  • $$15 : 14$$
  • $$9 : 10$$
  • $$2 : 3$$
  • $$3 : 5$$
A thin rod of mass $$6m$$ and length $$6L$$ is bent into regular hexagon. The $$M.I$$ of the hexagon about a normal axis to its plane and through centre of system is 
  • $$m{ L }^{ 2 }$$
  • $$3m{ L }^{ 2 }$$
  • $$5m{ L }^{ 2 }$$
  • $$11m{ L }^{ 2 }$$
A spherically symmetric gravitational system of particles has a mass density
$$\rho =\left\{\begin{matrix} \rho_0,\ \ r\leq R \\ 0,\ \  r > R\end{matrix}\right.$$ where $$\rho_0$$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance $$r(0 < r < \infty)$$ from the centre of the system is represented by.
Three identical masses each of mass $$1kg$$, are placed at the corners of an equilateral triangle of side $$l$$. Then the moment of inertia of this system about an axis along one side of the triangle is
  • 3$$Ml^2$$
  • $$l^2$$
  • $$\dfrac{3}{4}$$$$Ml^2$$
  • $$\dfrac{3}{2}$$ $$Ml^2$$
A thin rod of linear pass density $$ \lambda $$ at right angle at its mid point $$(C)$$ and fixed to points $$A$$ and $$B$$ such that it can rotate about an axis passing through $$AB$$ .The moment of inertia about an axis passing through $$AB$$ is :
1035106_185d543c8dd24aa49bb43090e91c8195.JPG
  • $$ \dfrac { \lambda l^3} {6 \sqrt2} $$
  • $$ \dfrac { \lambda l^3} {2 \sqrt2} $$
  • $$ \dfrac { \lambda l^3}{4} $$
  • $$ \dfrac { \lambda l^3}{ \sqrt2} $$
Initially two stable particles $$x$$ and $$y$$ start moving towards each other under mutual attraction. If at one time the velocities of $$x$$ and $$y$$ are $$V$$ and $$2V$$ respectively, what will be the velocity of centre of mass of the system?
  • $$V$$
  • Zero
  • $$\cfrac{V}{3}$$
  • $$\cfrac{V}{5}$$
A smooth horizontal rod passes through two identical rings, each of mass $$m$$. Rings are connected to a block of same mass through two strings of length $$2l$$ and $$l$$ as shown in figure. Block is released, when block is crossing lowest point its velocity is $$2\ m/s$$, velocity of left ring is
1029561_f8fde716523240f5858b927efd9dc3e0.png
  • $$4 \ m/s$$
  • $$2 \ m/s$$
  • $$3 \ m/s$$
  • $$None\ of\ these$$
Consider the following two statements:
(A) The linear momentum of a particle is independent of the frame of reference
(B) The kinetic energy of a particle is independent of the frame of reference
  • Both A and B are true
  • A is true but B is false
  • A is false but B is true
  • both A and B are false
If is the angular momentum is $$L$$ and $$I$$ is the moment of inertia of a rotating body, then $$ \dfrac { L^ 2 }{ 2I } $$ represents its ____________
  • rotational PE
  • total energy
  • rotational KE
  • translation KE
Find the moment of inertia of the triangular lamina of mass M about the axis of rotation AA' shown in the figure:
1059972_55e39b23fab14420a920697c82e87800.png
  • $$\frac{Ml^2}{3}$$
  • $$\frac{Ml^2}{6}$$
  • $$\frac{2}{3} Ml^2$$
  • $$\frac{1}{3} Ml^2$$
A uniform metal disc of radius R is taken and out of it a disc of diameter $$\dfrac{R}{2}$$ is cut off from the end.The centre of mass of the remaining part will be :
  • $$\dfrac{R}{28}$$ from the centre
  • $$\dfrac{R}{3}$$ from the centre
  • $$\dfrac{R}{5}$$ form the centre
  • $$\dfrac{R}{6}$$ from the centre
Th moment of inertia of a rod of mass $$M$$ and length $$L$$ about an axis passing through on edge of perpendicular to its length will be :-
  • $$\dfrac {ML^{2}}{12}$$
  • $$\dfrac {ML^{2}}{6}$$
  • $$\dfrac {ML^{2}}{3}$$
  • $$ML^{2}$$
A small block slides with velocity $$0.5 \sqrt gr$$ on the horizontal friction less surface as shown in the figure. The block leaves the surface at point $$C$$. The angle $$\theta$$ in the figure is:
1064255_21d45377cd11409bba9243f10079efd1.PNG
  • $$\cos^{-1} (4/9)$$
  • $$\cos^{-1} (3/4)$$
  • $$\cos^{-1} (1/2)$$
  • $$none\ of\ the\ above$$
Two blocks of masses $$2kg$$ and $$1kg$$ respectively are tied to the ends of a strings which passes over a light frictionless pulley. The masses are held at rest at the same horizontal level and then released. The distance traversed by centre of mass in $$2 $$ seconds is:($$g=10m/s^2$$)
1061653_ba6065d48fa44e03be792c2a76c7de64.png
  • $$1.42m$$
  • $$2.22m$$
  • $$3.12m$$
  • $$3.33m$$
In applying the equation for motion with uniform angular acceleration $$\omega =\omega _0+\alpha t$$ the radian measure 
  • Must be used for both $$\omega $$and $$\alpha$$
  • May be used for both $$\omega $$ and $$\alpha$$ `
  • may be used for $$\omega $$ but not $$\alpha$$
  • cannot be used for both $$\omega $$ and $$\alpha$$
Two particle A and B initially at rest move towards each other under a mutual force of attraction. At the instant when velocity of A is v and thata of B is $$2v$$, the velocity of centre of mass of the system 
  • $$v$$
  • $$2v$$
  • $$3v$$
  • Zero
The linear and angular acceleration of a particle are 10 m/$$sec^2$$ and 5 rad/$$sec^2$$ respectively. It will be at a distance from the axis of rotation
  • 50 m
  • $$\frac{1}{2} $$m
  • 1 m
  • 2 m
A solid sphere and a hollow sphere have same mass and radius. Ratio of radius of gyration of the solid sphere to that of the hollow sphere about a tangent axis is:
  • $$\sqrt {\frac{7}{3}} $$
  • $$\sqrt {\frac{3}{5}} $$
  • $$\sqrt {\frac{5}{3}} $$
  • $$\sqrt {\frac{{21}}{5}} $$
Two rods equal mass $$m$$ and length $$\ell$$ lie along the $$x$$ axis and $$y$$ axis with their centres origin. What is the moment of inertia of both about the line $$x = y$$ :
  • $$\dfrac{m\ell^2}{3}$$
  • $$\dfrac{m\ell^2}{4}$$
  • $$\dfrac{m\ell^2}{12}$$
  • $$\dfrac{m\ell^2}{6}$$
A wheel of mass $$10kg$$ has a moment of inertia of $$160kg -m^2$$  about its iwn axis. The radius of gyration is 
  • $$10m$$
  • $$4m$$
  • $$5m$$
  • $$6m$$
A body of mass $$5\ kg$$ is acted on by a net force $$F$$ which varies with time $$t$$ as shown in graph. Then the net momentum in $$SI$$ units gained by the body at the end of $$10$$ seconds is
1068067_b144c6ca75194277bf6d2b91cb2874eb.png
  • $$0$$
  • $$100$$
  • $$140$$
  • $$200$$
A triangular loop of side $$l$$ carries a current $$I$$. It is placed in a magnetic field $$B$$ such that the plane of the loop in the direction of $$B$$. The torque on the loop is:
  • Zero
  • $$IBl$$
  • $$\dfrac{\sqrt 3}{2} Il^2B^2$$
  • $$\dfrac{\sqrt 3}{4} B l^2$$
A ballet dancer, dancing on a smooth floor is spinning about a vertical axis with her arms folded with angular velocity of $$20\ rad/s$$. When the stretches her arms fully, the spinning speed decreases in $$10\ rad/s$$/. If $$I$$ is the initial  moment of inertia of the dancer, the new moment of inertia is
  • $$21$$
  • $$31$$
  • $$I/2$$
  • $$I/3$$
The velocity of centre of mass of system of block $$A,B$$ & $$C$$ is-
  • $$\dfrac {v_{0}}{2}$$
  • $$\dfrac {3v_{0}}{5}$$
  • $$\dfrac {2v_{0}}{5}$$
  • $$\dfrac {v_{0}}{5}$$
two identical particles move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of centre of mass is-
  • $$v$$
  • $$v/3$$
  • $$v/2$$
  • $$zero$$
0:0:1


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