CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 14 - MCQExams.com

For two masses $$10kg$$ and $$25kg$$, $$10m$$ apart, location of center of mass lies on
  • $$2.86m$$ from $$10kg$$
  • $$7.14m$$ from $$10kg$$
  • $$7.14m$$ from $$25kg$$
  • $$5m$$ from $$10kg$$
Three rods each of mass m and length l are joined together in the form of an equilateral triangle as shown. The moment of inertia about an axis along median of the triangle
1319474_63d525dbffcc4391b1b2e50f06771eeb.png
  • $$\frac{ml^2}{2}$$
  • $$\frac{ml^2}{4}$$
  • $$\frac{ml^2}{3}$$
  • $$\frac{2m^2}{3}$$
The radius of gyration of a body about an axis passing through its centre of mass is $$24 cm$$ . Calculate the radius of gyration of the body about a parallel axis passing through a point of a distance of $$7 \mathrm { cm }$$ from its centre of mass
  • $$25 \mathrm { cm }$$
  • $$20 \mathrm { cm }$$
  • $$0.25 \mathrm { cm }$$
  • $$2.5 \mathrm { cm }$$
A thin rod $$AB$$ of length $$l=1\ m$$ is such that its mass density increases uniformly from $$\rho$$ to $$A$$ to $$4\rho$$ at $$B$$, its total mass being $$M=30\ kg$$. The moment of inertia of the rod about the axis through $$A$$ perpendicular to $$AB$$ is:
  • $$13\ kg\ m^{2}$$
  • $$25\ kg\ m^{2}$$
  • $$18\ kg\ m^{2}$$
  • $$30\ kg\ m^{2}$$
Four particles each of mass $$m$$ are placed at the corners of a square of side length. The radius of gyration of the system about an axis perpendicular at the square and passing through centre is 
  • $$\frac{l}{{\sqrt 2 }}$$
  • $$\frac{l}{2}$$
  • $$l$$
  • $$l\sqrt 2 $$
A ring of radius R is rolling purely on the outer surface of a pipe of radius 4R. At some instant, the center of the ring has a constant speed=v. Then, the acceleration of the point on the ring which is in contact with the surface of the pipe is:
  • $$\dfrac{4v^{2}}{5R}$$
  • $$\dfrac{3v^2}{5R}$$
  • $$\dfrac{v^{2}}{4R}$$
  • $$zero$$
Two rings of same mass and thickness , but different densities rotate about their axis of rotation on applying same torque . If the ration of their densities is 4:1, then the ratio of their angular acceleration will be
  • 16:1
  • 1:16
  • 4:1
  • 1:4
A thick hollow sphere rolls down a rough inclined plane without slipping and reaches the bottom with speed $$v _ { 0 } ,$$ when it is again released on a similar but smooth inclined plane, it reaches the bottom with $$\dfrac { 5 v _ { 0 } } { 4 }$$ the radius of gyration of sphere about an axis through its center is ( $$R$$ is the radius of outer surface of the sphere)
  • $$\dfrac { 4 R } { 5 }$$
  • $$\dfrac { 3 R } { 5 }$$
  • $$\dfrac { 3 R } { 4 }$$
  • $$\dfrac { R } { 2 }$$
The angular speed of a body changes from $$ \omega_1 $$ to $$ \omega_2 $$ without applying a torque but due to change in its moment of inertia.the ratio of radii of gyration in the two cases is
  • $$ \sqrt \omega_2 : \sqrt \omega_1 $$
  • $$ \sqrt \omega_1 : \sqrt \omega_2 $$
  • $$ \omega_1 : \omega_2 $$
  • $$ \omega_2 : \omega_1 $$
A simple pendulum of mass $$m$$ executes $$SHM$$ with total energy $$E$$. If at an instant it is at one of extreme positions, then its linear momentum after a phase shift of $$\dfrac { \pi  }{ 3 }\ rad$$ will be
  • $$\sqrt { 2mE } $$
  • $$ \dfrac { \sqrt{3mE} }{ 2 }$$
  • $$\sqrt { \dfrac { 2mE }{ 3 } } $$
  • $$2\sqrt { mE } $$
Four masses are joined to a light circular frames in the figure. The radius of gyration of this system about an axis passing through the centre of the circular frame and perpendicular to its plane would be (where a is the radius of the circle)
1322230_ca19091331714a5abe4766ff302934b3.png
  • $$\dfrac { a }{ \sqrt { 2 } } $$
  • $$\dfrac a 2$$
  • $$a$$
  • $$2a$$
A child is standing at one end of long trolley moving with a speed V on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u the centre of mass of the system(trolley +child) will move with a speed 
  • $$(v-u)$$
  • $$v$$
  • $$(v+u)$$
  • $$zero$$
For a particle showing motion under the force $$F=-5{ \left( x-2 \right) },$$ the motion is
  • Translatory
  • Oscillatory
  • SHM
  • Both (2) & (3)
A cylinder rolls without slipping on a rough horizontal floor, its centre of mass moving with a speed $$v$$. It makes an elastic collision with smooth vertical wall. After impart.
  • Its centre of mass will move with a speed $$v$$ initially
  • Its motion will be rolling without slipping
  • Its motion will be rolling with slipping initially and its rotational motion will stop momentarily at some instant
  • Its motion will be rolling without slipping only after some time
A disc rolls on ground without slipping. Velocity of centre of mass is v. The speed of particle P at circumference $$(v_p)$$ is
1321346_c6760b999ab24b8d985a331f0655b999.png
  • v
  • $$\sqrt 2 v$$
  • 2v
  • $$\sqrt 3 v$$
$$1 J$$ of work is required to stop an iron rim from rolling on a horizontal floor.The mass and the radius of the rim are $$3 \text { kg and } 40 \mathrm { cm }$$ respectively. What is the speed of the centre of mass of the rim?
  • $$19 \mathrm { cm } / \mathrm { s }$$
  • $$27 \mathrm { cm } / \mathrm { s }$$
  • $$58 \mathrm { cm } / \mathrm { s }$$
  • $$89 \mathrm { cm } / \mathrm { s }$$
In the figure shown $$ABC$$ is a uniform wire. If centre of mass of wire lies vertically below point $$A$$, then $$\cfrac{BC}{AB}$$ is close to:
  • $$1.85$$
  • $$1.37$$
  • $$1.5$$
  • $$3$$
A rectangular plate is placed on a rough plank. Dimensions of the plank is as shown in the figure. Find the minimum acceleration with which the plank should be moved so that the rectangular plate topples (consider the friction is sufficient so the plate does not slide).
1323630_39ea62deb0834a84ba5f18eae487b78e.jpg
  • $$g$$
  • $$\dfrac {g}{2}$$
  • $$\dfrac {g}{5}$$
  • Block will never topples
A light rod of length $$l$$ has two masses $$m_1$$ and $$m_2$$ attached to its two ends. The moments of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is:-
  • $$\sqrt {{m_1}{m_2}} {l^2}$$
  • $$\frac{{{m_1}{m_2}}}{{{m_1} + {m_2}}}{l^2}$$
  • $$\frac{{{m_1} + m + 2}}{{{m_1}{m_2}}}{l^2}$$
  • $$({m_1} + {m_2}){l^2}$$
Four masses m, 2m, 3m, & 4m, are kept on a straight line at 0, a, 2a & 3a as shown in figure. The radius of gyration of the system about axis AB is
  • $$\sqrt { 2 } a$$
  • $$\sqrt { 3 } a$$
  • 2 a
  • $$\sqrt { 5 } a$$
Three particles, each of mass $$m$$ are situated at the vertices of an equilateral triangle $$ABC$$ of side $$l$$ (as shown in the figure). 
The moment of inertia of the system about a line $$AX$$ perpendicular to $$AB$$ and in the plane of $$ABC$$, will be:
1353255_f4d2105882d743e2a4b5d0dfc9ab531a.PNG
  • $$2 ml^2$$
  • $$\frac {5}{4} ml^2$$
  • $$\frac {3}{2} ml^2$$
  • $$\frac {3}{4} ml^2$$
The moment of inertia of hollow cylinder of mass $$M$$ and radius $$R$$ about its axis of rotation is $$MR^{2}$$. The radius of gyration of the cylinder about the axis is
  • $$\dfrac {R}{\sqrt {2}}$$
  • $$\sqrt {2}R$$
  • $$R$$
  • $$\dfrac {R}{2}$$
A flexible chain of length 2m and mass 1 kg initially held in vertical position such that its lower end just touches a horizontal surfaces, is released from rest at time t=0, Assuming that any part of chain which strike the plane immediately comes to rest and that the portion of chain lying on horizontal surface does not form  any heap, the height of its center of mass above surface at any instant $$t=1/\sqrt { 5 } $$(before it completely comes to rest) is
  • 1 m
  • 0.5 m
  • 1.5 m
  • 0.25 m
A solid sphere rolls down an inclined plane and its velocity at the bottom is $${ v }_{ 1 }$$. The same sphere slides down the plane (without friction) and its velocity at the bottom is $${ v }_{2 }$$. Which of the relations given below is correct?
  • $${ v }_{ 1 }={ v }_{ 2 }$$
  • $${ v }_{ 1 }=\sqrt { \frac { 5 }{ 7 } } { v }_{ 2 }$$
  • $${ v }_{ 1 }=\sqrt { \frac { 7 }{ 5 } } { v }_{ 2 }$$
  • None of these
An insulating thin rod of length $$l$$ as a $$x$$ linear charge density $$p(x) = \rho_{0} \dfrac {x}{l}$$ on it. The rod is rotated about an axis passing through the origin $$(x = 0)$$ and perpendicular to the rod. If the rod makes $$n$$ rotations per second, then the time averaged magnetic moment of the rod is
  • $$\dfrac {\pi}{4}n\rho l^{3}$$
  • $$n\rho l^{3}$$
  • $$\pi n\rho l^{3}$$
  • $$\dfrac {\pi}{3}n\rho l^{3}$$
The moment of inertia of composite rod about an axis perpendicular to its length and passing through its center is
1360560_f799223eae2c4a1d8b35be9bc95c54c6.png
  • $$\left( { m }_{ 1 }+{ m }_{ 2 } \right) \left( \dfrac { { l }_{ 1 }^{ 2 } }{ 3 } +\dfrac { { l }_{ 2 }^{ 2 } }{ 3 } \right) $$
  • $$\left( { m }_{ 1 }+{ m }_{ 2 } \right) \left( \dfrac { { l }_{ 1 }^{ 2 } }{ 12 } +\dfrac { { l }_{ 2 }^{ 2 } }{ 12 } \right)$$
  • $$\dfrac { { \left( { m }_{ 1 }+{ m }_{ 2 } \right) \left( { l }_{ 1 }+{ l }_{ 2 } \right) }^{ 2 } }{ 12 } $$
  • $$\dfrac { { m }_{ 1 }{ l }_{ 1 }^{ 2 } }{ 3 } +\dfrac { { m }_{ 2 }{ l }_{ 2 }^{ 2 } }{ 3 } $$
Six identical particles each of mass 'm' are arranged at the corners of a regular hexagon of side length "L". If the mass of one of the particle is doubled, the shift in the center of mass is
  • $$L$$
  • $$6L/7$$
  • $$L/7$$
  • $$\cfrac{L}{\sqrt{3}}$$
A rod weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is
  • $$\frac{W\left ( d-x \right )}{d}$$
  • $$\frac{Wx}{d}$$
  • $$\frac{Wd}{s}$$
  • $$\frac{W\left ( d-x \right )}{x}$$
Two objects initially some distance apart are released from rest. They move towards each other under mutual gravitational force. At some instant, speed of one of them is $$v$$ and that of other is $$v / 4$$ .Then speed of their centre of mass at this instant is: 
  • $$\cfrac { 3 v } { 4 }$$
  • $$\cfrac { v } { 4 }$$
  • $$\cfrac { 5 v } { 4 }$$
  • zero
Find the moment of inertia of three identical rods each of mass $$m$$ and length $$l$$ forming an equilateral triangle, about one of its sides
1361362_67372dd7f75a4b22bf65091c54443850.PNG
  • $$\dfrac {ml^2}{4}$$
  • $$\dfrac {ml^2}{2}$$
  • $$\dfrac {3ml^2}{4}$$
  • $$\dfrac {2ml^2}{3}$$
A body of mass 5 kg initially moving with speed 10 m/s along x-axis in gravity free space explodes and breaks into three pieces of masses 1 kg, 1 kg and 3 kg. the two pieces of equal masses fly off with the same speed 20 m/s along y-axis and z-axis respectively. what is the velocity of heavier fragment?
  • $$ ( \frac {10}{3} \hat i - \frac {20}{3} \hat j - \frac {40}{3} \hat k ) m/s $$
  • $$ ( \frac {50}{3} \hat i - \frac {20}{3} \hat j - \frac {20}{3} \hat k ) m/s $$
  • $$ ( \frac {20}{3} \hat i - \frac {20}{3} \hat j - \frac {20}{3} \hat k ) m/s $$
  • None
Three identical rods, each of mass $$m$$ and length $$l$$ , form an equilateral triangle . Moment of inertia about one of the sides is:
  • $$\frac { m l ^ { 2 } } { 4 }$$
  • $$\frac { 2 } { 3 } m l ^ { 2 }$$
  • $$\frac { 3 m l ^ { 2 } } { 4 }$$
  • $$\frac { m l ^ { 2 } } { 2 }$$
Half of the rectangular plate shown in figure is made of a material of density $$\rho _ { 1 }$$ and the other half of density $$\rho _ { 2 }$$.The length of the plate is $$L$$. Locate the centre of mass of the plate.
1374883_722d6082caaf4ba7ae3b50a27aee6b38.png
  • $$\cfrac { \left( \rho _ { 1 } + 3 \rho _ { 2 } \right) L } { 4 \left( \rho _ { 1 } + \rho _ { 2 } \right) }$$
  • $$\cfrac { \left( \rho _ { 1 } + 3 \rho _ { 2 } \right) L } { 2 \left( \rho _ { 1 } + \rho _ { 2 } \right) }$$
  • $$\cfrac { \left( 3 \rho_ { 1 } + \rho _ { 2 } \right) L } { 2 \left( \rho _ { 1 } + \rho _ { 2 } \right) }$$
  • none
Calculate the moment of inertia of the given rod about an axis AB
1364206_e150f9bfad874eef9c774690d5ff4ea7.png
  • $$\frac{ML^2}{12}$$
  • $$\frac{ML^2}{3}$$
  • $$\frac{4ML^2}{9}$$
  • $$\frac{7ML^2}{36}$$
A uniform rod AB of mass M and length L is hinged at one end A. It is released from rest at a horizontal position. The linear acceleration of the centre of mass when it starts to fall is 
  • $$\dfrac{g}{4}$$
  • $$\dfrac{g}{2}$$
  • $$g$$
  • $$\dfrac{3g}{4}$$
The position of axis of rotation of a body is changed so that its moment of inertia decreases by 36$$\%$$ . The $$\%$$ change in itsradius of gyration is 
  • decreases by 18$$\%$$
  • increases by 18$$\%$$
  • decreases by 20$$\%$$
  • increases by 20$$\%$$
Two bodies of different masses  $$2 \mathrm{kg}  $$ and $$4  \mathrm{kg} $$ are moving with velocities $$2  \mathrm{m} / \mathrm{s}  $$ and $$10  \mathrm{m} / \mathrm{s}  $$ towards each other due to mutual gravitational attraction.Then the velocity of the centre of mass is
  • $$5 \mathrm{ms}^{-1} $$
  • $$6 \mathrm{ms}^{-1} $$
  • $$8 m s^{-1} $$
  • Zero
Three identical rods each of mass m and length $$\ell$$  are joined to form an equilateral triangle. The moment of inertia about an axis passing through one corner and perpendicular to the plane of triangle, is
  • $$\frac { 4 } { 3 } m \ell ^ { 2 }$$
  • $$\frac { 9 } { 8 } m \ell ^ { 2 }$$
  • $$\frac { 3 } { 4 } m \ell ^ { 2 }$$
  • $$\frac { 3 } { 2 } m \ell ^ { 2 }$$
A metallic ball has spherical cavity at its centre. If the ball is heated, what happens to the cavity?
  • its volume increases
  • its volume decreases
  • its volume remains unchanged
  • its volume may decreased or increase depending upon the nature of metal
Locate centre of mass of a uniform semicircular loop of radius R (shown in figure)
1410250_a0a7b62ea17a4b25ab7c398e51cc00e3.PNG
  • $$\frac{2 \ R}{\pi} \ above \ C_1$$
  • $$\frac{2 \ R}{2 + \pi}\ above \ C_1$$
  • $$\frac{R}{2 + \pi} \ above \ C_1$$
  • $$\frac{3 \ R}{2 + \pi} \ above \ C_1$$
A uniform wire of length $$\ell $$ is bent into the shape of 'V' as shown. the distance of its centre of mass from the vertex A is  

Given (length AB = AC)

1393214_f9f33ab8ab7e4a0185e11becd2eb535b.JPG
  • $$\L /2$$
  • $$\dfrac { \L \sqrt { 3 } }{ 4 } $$
  • $$\dfrac { \L \sqrt { 3 } }{ 8 } $$
  • None of these
A particle  $$P$$  strikes the rod  $$R$$  perpendicularly as shown. The rod is suspended vertically with upper end hinged $$\left( x = \dfrac { 1 } { 2 } , \text { elastic collision } \right)$$  Then select correct statement:
1405003_0bfc6d964ea04b83b76d6becf344b8ac.png
  • Linear momentum of $$P.R$$ system increases
  • Linear momentum of $$P.R$$ system decreases
  • Linear momentum of $$P.R$$ system remains constant
  • None of these
A uniform thick plate in the shape of an arrow head has dimensions as shown in the given figure. The centre of mass lies at a point.
1406108_ef8d9133097443429cbafa9ee04be12b.PNG
  • 1.5 cm to the right of O
  • 3 cm to the right of O
  • O itself
  • 1 cm to the right of O
A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the centre of the disc, the distance $$x_2$$ of the centre of mass of the remaining part from the initial centre of mass O is given by:-
1409708_40d77077087049b4889b55ecbf47ce04.png
  • $$\frac{\pi b^2}{(a^2- b^2)}$$
  • $$\frac{-c b^2}{(a^2- b^2)}$$
  • $$\frac{\pi c^2}{(a^2- b^2)}$$
  • $$\frac{\pi a^2}{(c^2- b^2)}$$
A disc of radius r rolls on without slipping on a rough horizontal floor. If velocity of its centre of mass is v then velocity of point p, as shown in the figure $$\left[ O P = \left( \cfrac { r } { 2 } \right) \text { and } \angle Q O P = 60 ^ { \circ } \right]$$  is-

1390666_1b9c6586dabd403ba99248c6fb07b3f2.jpg
  • $$\left( \cfrac { v _ { 0 } } { 2 } \right) \sqrt { 7 }$$
  • $$\left( \cfrac { v _ { 0 } } { 2 } \right) \sqrt { 3 }$$
  • $$\mathrm { v } _ { 0 }$$
  • $$\left( \cfrac { v _ { 0 } } { 2 } \right)$$
Two rods of equal mass m and length $$l$$ lie along the $$  x  $$ axis and $$  y  $$ axis with their centres at the origin.What is the moment of inertia of both about the line $$  x=y : $$
  • $$ \frac{m l^{2}}{3} $$
  • $$ \frac{m l^{2}}{4} $$
  • $$ \frac{m l^{2}}{12} $$
  • $$ \frac{m l^{2}}{6} $$
Select correct statement  regarding centrn of mass 
  • In uniform symmetrical body it coincides with geometrical centre
  • It necessarily lies at centre of gravity
  • In center of mass frame momentum of system is zero
  • Both (1) & (3)
A uniform metre rule of mass 100$$\mathrm { g }$$ is balanced on afulcrum at mark 40$$\mathrm { cm }$$ by suspending an unknownmass $$m$$ at the mark 20$$\mathrm { cm } .$$ 
  • Find the value of $$m$$
  • To which side the rule will tilt if the mass $$m$$ is
    moved to the mark 10$$\mathrm { cm } ?$$
  • What is the resultant moment now?
  • How can it be balanced by another mass of
    50$$\mathrm { g } ?$$
A disk and a ring of the same mass are rolling to have the same kinetic energy. What is ratio of the velocities of centre of mass
  • $$( 4 : 3 ) ^ { 1 / 2 }$$
  • $$( 3 : 4 ) ^ { 1 / 2 }$$
  • $$( 2 ) ^ { 1 / 2 } : ( 3 ) ^ { 1 / 2 }$$
  • $$( 3 ) ^ { 1 / 2 } : ( 2 ) ^ { 1 / 2 }$$
Three identical thin rods each of length 'l' and mass M are joined together to from a ladder H. What is the moment of inertia of the system about one of the sides of H?
  • $$ \frac { Ml^{ 2 } }{ 4 } $$
  • $$ \frac { Ml^{ 2 } }{ 3 } $$
  • $$ 2\frac { Ml^{ 2 } }{ 3 } $$
  • $$ 4\frac { Ml^{ 2 } }{ 3 } $$
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