CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 8 - MCQExams.com

A particle of mass M kg describes a circle of radius 1 m. The centripetal acceleration of the particle is $$ 4m/s^2 $$. What will be the momentum of the particle ?
  • 4 M
  • 2 M
  • 8 M
  • M
Four rings each of mass $$M$$ and radius $$R$$ are arranged as shown in the figure. The moment of inertia of the system about the axis $$yy'$$ is 
1179527_f1dec03149e4462995efde354b8d0e11.png
  • $$2 M R ^ { 2 }$$
  • $$3 M R ^ { 2 }$$
  • $$4 M R ^ { 2 }$$
  • $$5 M R ^ { 2 }$$
Three identical thin rods each of length l and mass M are joined together to from a letter H. What is the moment of intertia of the system about one of the sides of H
  • $$\dfrac{Ml^{2}}{3}$$
  • $$\dfrac{Ml^{2}}{4}$$
  • $$\dfrac{2Ml^{2}}{3}$$
  • $$\dfrac{4Ml^{2}}{3}$$
A body of mass $$3$$ kg is thrown from ground with a speed $$10$$ m/s at an angle $$53^0$$ with horizontal. At the highest point of its path it is fragmented into three identical pieces such that one of them comes to rest. Velocity of the centre of mass just after fragmentation is
  • $$10$$ m/s
  • $$5$$ m/s
  • $$6$$ m/s
  • $$8$$ m/s
Two bodies of masses $$2kg$$ and $$4kg$$ are moving with velocities $$2m/s$$ and $$10m/s$$ respectively towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass (Bodies are at rest initially) :
  • $$5.3\ m/s$$
  • $$6.4\ m/s$$
  • $$zero$$
  • $$8.1\ m/s$$
A meter stick is placed vertically at the origin on a frictionless surface. A gentle push in x direction is given to the top most point of the rod, when it has fallen completely $$x\ coordinate$$ of center of rod is at:
  • $$origin$$
  • $$-0.5\ m$$
  • $$-1\ m$$
  • $$+0.5\ m$$
Two spherical bodies of mass $$M$$ and $$5M$$ and radii $$R$$ and $$2R$$ respectively are released in free space with initial separation between their centers equal to $$12R$$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before the collision is
1201008_d9336371930540bca17269fd362381d3.png
  • $$4.5\ R$$
  • $$7.5\ R$$
  • $$1.5\ R$$
  • $$2.5\ R$$
The position of axis of rotation of a body is changed so that its moment of inerted decreases by 36%. The % change in the radius of gyration is  
  • decreases by 18%
  • increases by 18%
  • decreases by 20%
  • increases by 20%
A satellite is revolving around a planet in a circuit orbit of radius. $$'r'$$ and has angular momentum $$L$$. If it is taken into a higher orbit of radius $$'4r'$$, the charge in its angulatr momentum is
  • $$ L/4$$
  • $$L/2$$
  • $$3L/4$$
  • $$L$$
The radius of gyration of hollow sphere of radius R w.r.t triangle axis on it is
  • $$\sqrt{\dfrac{7}{5}}R$$
  • $$\sqrt{\dfrac{7}{3}}R$$
  • $$\sqrt{\dfrac{2}{5}}R$$
  • $$\sqrt{\dfrac{2}{3}}R$$
Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitation attraction. The speed of each particle with respect to their centre of mass is :
  • $$\sqrt { \dfrac { Gm }{ 4R } } $$
  • $$\sqrt { \dfrac { Gm }{ 3R } } $$
  • $$\sqrt { \dfrac { Gm }{ 2R } } $$
  • $$\sqrt { \dfrac { Gm }{ R } } $$
Length width and mass of a rectangular plate are l, b and m respectively. The radius of gyration about the axis passing through centre and perpendicular to the plane is -
  • $$\sqrt { \frac { { l }^{ 2 }+{ b }^{ 2 } }{ 2 } } $$
  • $$\sqrt { \frac { { l }^{ 2 }+{ b }^{ 2 } }{ 8 } } $$
  • $$\sqrt { \frac { { l }^{ 2 }+{ b }^{ 2 } }{ 10 } } $$
  • $$\sqrt { \frac { { l }^{ 3 }+{ b }^{ 3 } }{ 10 } } $$
A football roots through the ground. The path followed by centre of mass of football is 
  • Linear
  • Circular
  • Rotational
  • All the above
A circular loop of radius $$0.3\ cm$$ lies parallel to a much bigger circular loop of radius $$20\ cm$$. The centre of the smaller loop is on the axis of the bigger drop. The distance between their centres is $$15\ cm$$. If a current of $$10\ A$$ flows through the bigger loop, then the flux linked with smaller loop is
  • $$9.1\times 10^{-11} Wb$$
  • $$6\times 10^{-11} Wb$$
  • $$3.3\times 10^{-11} Wb$$
  • $$6.6\times 10^{-11} Wb$$
A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has the velocity of 2m/s and 3kg body has 7m/s. The velocity of the centre of mass at that instant is :-
  • 5 m/s
  • 1 m/s
  • 0
  • $$\frac { 12 }{ 5 } m/s$$
In the figure as shown pulley is light and massless thread is having two masses at their ends. Then the acceleration of centre of mass of two blocks is 
1221933_51683e92dbbd4cb0bdecf676ea897b53.png
  • $$\cfrac{g}{5}$$
  • $$\cfrac{g}{10}$$
  • $$\cfrac{3g}{5}$$
  • $$\cfrac{g}{4}$$
A solid sphere is thrown on a horizontal rough surface with initial velocity of centre of mass u  without rolling. Velocity of its centre of mass when it starts pure rolling is 
  • $$\frac{{3u}}{5}$$
  • $$\frac{{2u}}{5}$$
  • $$\frac{{5u}}{7}$$
  • $$\frac{{2u}}{7}$$
A couple produces,_____
  • pure rotation
  • pure translation
  • rotation and translation
  • no motion

A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break 

  • (a) when the mass is at the highest point.

  • (b) when the mass is at the lowest point.

  • (c) when the wire is horizontal

  • (d) at an angle of cos⁻¹(1/3) from the upward vertical.

A uniform rod of length l and mass M rotating about a fixed vertical axis on a smooth horizontal table. It elastically strikes a particle placed at a distance l/3 from its axis and stops. Mass of the particle is   
1234159_f89e43b937d84d27857f0f0f2b048aef.PNG
  • 3M
  • $$\dfrac{3M}{4}$$
  • $$\dfrac{3M}{2}$$
  • $$\dfrac{4M}{3}$$
A rod $$0.5$$ m long has two masses each of $$20$$ gram stuck at its ends. If the masses are treated as point masses and if the mass of the rod is neglected, then the moment of inertia of the system about a transverse axis passing through the centre is 
  • $$1.25 \times 10 ^ { - 3 } \mathrm { kg } - \mathrm { m } ^ { 2 }$$
  • $$2.5 \times 10 ^ { - 3 } \mathrm { kg } - \mathrm { m } ^ { 2 }$$
  • $$4 \times 10 ^ { - 3 } \mathrm { kg } - \mathrm { m } ^ { 2 }$$
  • $$5 \times 10 ^ { - 3 } \mathrm { kg } - \mathrm { m } ^ { 2 }$$
A ring takes time $$t_1$$ in slipping down an inclined plane of length L, whereas it takes time $$t_2$$ in rolling down the same plane. The ratio of $$t_1$$ and $$t_2$$ is :
  • $$2^{\frac {1} {2}}:1$$
  • $$1: 2^{\frac {1} {2}}$$
  • $$1:2$$
  • $$1:2^{\frac{1} {4}}$$
Eight point masses m that are held in a cubical array by rods of length 1 (whose masses are negligible). Find the moments of inertia of the system about the following axes 
  • an axis parallel to one face passing through the center of the cube;
  • an axis coinciding with one edge;
  • an axis passing through the centers of opposite edges of one face; and
  • an axis passing through diagonally opposite corners of one face.
Four bodies of masses 1,2,3,4 kg respectively are placed at the corners of a square of side $$'a'$$. Coordinates of centre of mass are (take $$1\ kg$$ at origin, $$2\ kg$$ on X-axis and $$4\ kg$$ on Y-axis)
  • $$\Big \lgroup \dfrac{7a}{10}, \dfrac{a}{2} \Big \rgroup$$
  • $$\Big \lgroup \dfrac{a}{2}, \dfrac{7a}{10} \Big \rgroup$$
  • $$\Big \lgroup \dfrac{a}{2}, \dfrac{3a}{10} \Big \rgroup$$
  • $$\Big \lgroup \dfrac{7a}{10}, \dfrac{3a}{2} \Big \rgroup$$
$$16\ kg$$ and $$9\ kg$$ are separated by $$25\ cm$$. The velocity with which a body should be projected from the midpoint of the line joining the two masses so that it just escape is : 
  • $$\sqrt{g}$$
  • $$\sqrt{2gR}$$
  • $$2\sqrt{G}$$
  • $$2\sqrt{g}$$
Two blocks of masses $$8$$kg are connected by a spring of negligible mass and placed on a frictions less horizontal surface. An impulse gives a velocity of $$12$$m/s to the heavier block in the direction of lighter block. The velocity of the center of mass is:-
  • $$12$$m/s
  • $$10$$m/s
  • $$8$$m/s
  • $$6$$m/s
Consider a system having two masses $$m_{1}$$ and $$m_{2}$$ in which first mass is pushed towards the center of mass by a distance $$a$$. The distance by which the second should be moved to keep the center of mass at same position is
1242098_2db97b107bb14e86917fa5e010680ece.png
  • $$\dfrac{m_{1}}{m_{2}}a$$
  • $$\dfrac{m_{1}}{(m_{1}+m_{2})}a$$
  • $$\dfrac{m_{2}}{m_{1}}a$$
  • $$\left(\dfrac{m_{2}}{(m_{1}+m_{2})}\right)a$$
The ratio of the radii of gyration of a circular disc to that of circular ring, each of same mass and same radius about axes is 
  • $$\sqrt { 3 } :\sqrt { 2 } $$
  • $$1:\sqrt { 2 } $$
  • $$\sqrt { 2 } :1$$
  • $$\sqrt { 2 } :\sqrt { 3 } $$
A thin uniform rod of length l and m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $$\omega$$. Its centre of mass rises to a maximum height of:
  • $$\dfrac{1}{6} \dfrac{l\omega}{g}$$
  • $$\dfrac{1}{2} \dfrac{l^2\omega^2}{g}$$
  • $$\dfrac{1}{6} \dfrac{l^2\omega^2}{g}$$
  • $$\dfrac{1}{3} \dfrac{l^2\omega^2}{g}$$

Linear mass density of a rod AB ( of length 10 m) varies with distance x from its end A as $$\lambda  = {\lambda _o}{x^3}$$$$\left( {{\lambda _o}\;{\text{is}}\;{\text{positive}}\;{\text{constant}}} \right)$$. Distance of the center of mass of the rod, from end B is
  • 8 m
  • 2 m
  • 6 m
  • 4 m
If the moment of inertia of a rigid body is numerically equal to its mass, its radius of gyration is  
  • Equal to its radius
  • Equal to diameter
  • Equal to one unit
  • none
A slender uniform rod of mass $$M$$ and length $$l$$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $$\theta$$ with the vertical is:
1265860_7d5e87e2d4c447c49cda7d444b1a9e40.PNG
  • $$\cfrac{3g}{2l}\cos{\theta}$$
  • $$\cfrac{2g}{3l}\cos{\theta}$$
  • $$\cfrac{3g}{2l}\sin{\theta}$$
  • $$\cfrac{2g}{3l}\sin{\theta}$$

Find the coordination of center of mass of a uniform semicircle closed wire frame with respect to the origin which is at its center.The radius of the circular portion is R.                
  • $$\left( {\dfrac{{4R}}{{3\pi }},0} \right)$$
  • $$\left( {\dfrac{{2R}}{{\pi }},0} \right)$$
  • $$\left( {\dfrac{R}{{\pi + 2}},0} \right)$$
  • $$\left( {\dfrac{2R}{{\pi + 2}},0} \right)$$
A rod of length I is held vertically stationary with its lower end located at a point 'P', on the horizontal plane. When the rod is released to topple about 'P', the velocity of the upper end of the rod with which it hits the ground is 
  • $$\sqrt { \frac { g } { l } }$$
  • $$\sqrt { 3 g l }$$
  • $$3 \sqrt { \frac { g } { l } }$$
  • $$\sqrt { \frac { 3 g } { l } }$$
$$A = ( 2,3,5 ) ; B = ( - 1,3,2 ) ; C = ( \lambda , 5 , \mu )$$ are the vertices of a triangle. If the median $$AM$$ is equally inclined to the coordinate axes, then $$( \lambda , \mu ) =$$
  • $$( 10,7 )$$
  • $$( -10,7 )$$
  • $$( 7,10 )$$
  • $$( -7,-10 )$$
Four holes of radius $$R$$ are cut from a thin square plate of  side $$4R$$ and mass $$M$$.Determine inertia of the remaining portion about z-axis.
  • $$\left[ {\dfrac{{10\pi }}{{16}} - \dfrac{8}{3}} \right]\;M{R^2}$$
  • $$\left[ {\dfrac{{8\pi }}{{3}} - \dfrac{10}{16}} \right]\;M{R^2}$$
  • $$\left[ {\dfrac{{10\pi }}{{3}} - \dfrac{10}{16}} \right]\;M{R^2}$$
  • $$\left[ {\dfrac{{10\pi }}{{16}} - \dfrac{10}{3}} \right]\;M{R^2}$$
A disc of mass $$10kg$$ has moment of inertia of $$90kg$$ $${m}^{2}$$ about the axis which lies in the plane of disc and passing through its centre. The radius of gyration of disc about this axis is
  • $$3m$$
  • $$\cfrac{3}{\sqrt{2}}m$$
  • $$\cfrac{3}{2}m$$
  • $$\sqrt{\cfrac{3}{2}}m$$
Four particles each of mass $$m$$ are placed at the corners of a square of side length $$l$$. The radius of gyration of the system about an axis perpendicular to the square and passing through centre is :-
  • $$\dfrac{l}{\sqrt{2}}$$
  • $$\dfrac{l}{2}$$
  • $$l$$
  • $$l\sqrt{2}$$
Two particles having mass ratio n : 1 are interconnected by a light in extensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is
  • $$( n - 1 ) ^ { 2 } g$$
  • $$\left( \frac { n + 1 } { n - 1 } \right) ^ { 2 } g$$
  • $$\left( \frac { n - 1 } { n + 1 } \right) ^ { 2 } g$$
  • $$\left( \frac { n + 1 } { n - 1 } \right) 9$$
The moment of inertia of two equal masses each of mass m at separation l connected by a rod of mass M. about an axis passing through centre and perpendicular to length of rod is.
  • $$\dfrac{{\left( {M + 3m} \right){L^2}}}{{12}}$$
  • $$\dfrac{{\left( {M + 6m} \right){L^2}}}{{12}}$$
  • $$\dfrac{{M{L^2}}}{4}$$
  • $$\dfrac{{M{L^2}}}{12}$$
The moment of inertia of a uniform cylinder of length $$l$$ and radius $$R$$ about its perpendicular bisector is $$1$$. What is the ratio $$l/R$$ such that the moment of inertia is minimum?
  • $$\cfrac{3}{\sqrt{2}}$$
  • $$\sqrt{\cfrac{3}{2}}$$
  • $$\cfrac{\sqrt{2}}{2}$$
  • $$1$$
A diatomic molecule is formed by two atoms which may be treated as mass points $${m}_{1}$$ and $${m}_{2}$$, joined by a massless rod of length $$r$$. Then the moment inertia of the molecule about an axis passing through the centre of mass and perpendicular to rod is
  • zero
  • $$({m}_{1}+{m}_{2}){r}^{2}$$
  • $$\left( \cfrac { { m }_{ 1 }+{ m }_{ 2 } }{ { m }_{ 1 }{ m }_{ 2 } } \right) {r}^{2}$$
  • $$\left( \cfrac { { m }_{ 1 }{ m }_{ 2 } }{ { m }_{ 1 }+{ m }_{ 2 } } \right) {r}^{2}$$
Three identical rods, each of length $$l$$, are joined to from a rigid equilateral triangle. its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is
  • $$\cfrac {l}{2}$$
  • $$ \sqrt {\cfrac {3l}{2}}$$
  • $$\cfrac {l}{\sqrt {2}}$$
  • $$\cfrac {l}{\sqrt 3}$$
Six identical particles each of mass $$m$$ are arranged at the corners of a regular hexagon of side length $$a$$. If the mass of one of the particle is doubled, the shift in the centre of mass is
  • $$a$$
  • $$\dfrac {6a}{7}$$
  • $$\dfrac {a}{7}$$
  • $$\dfrac {a}{\sqrt {3}}$$
In rotational motion of a rigid body, all particle move with
  • Same linear and angular velocity
  • Same linear and different angular velocity
  • With different linear velocities and same angular velocities
  • With different linear velocities and different angular velocities
A disc of radius 2 m and mass 200 kg is acted upon by a torque 100 N-m Its angular acceleration would be
  • 1 rad/$${ sec }^{ 2 }$$
  • 0.25 rad/$${ sec }^{ 2 }$$
  • 0.5 rad/$${ sec }^{ 2 }$$
  • 2 rad/$${ sec }^{ 2 }$$
A ight rod one meter long has two point masses,0.1 kg each, fixed at its ends. the moment of inertia of the system about a transverse axis through its centre of mass is
  • $$ 5 kg \cdot m^3 $$
  • $$ 0.25 kg \cdot m^2 $$
  • $$ 0.05 kg \cdot m^2 $$
  • $$ 0.025 kg \cdot m^2 $$
Three identical masses are kept at the corners of an equilateral triangle ABC. A moves towards B with a velocity V, B moves towards C with velocity V, and C moves towards A with same velocity V. Then the velocity of center of mass of the system of particles is 
  • V
  • zero
  • 3V
  • $$\dfrac { V }{ 3 } $$
Earth is flattened at the poles and bulges at the equator. This is due to the fact that 
  • the earth revolves around the sun in an elliptical orbit,
  • the angular velocity of spinning about its axis is more at the equator.
  • the centrifugal force is more at the equator than at poles.
  • None of these.
The motion of the center of mass of a system of two particles is unaffected by their internal forces
  • Irrespective of then actual directions of the internal forces
  • only if they are along the line joining the particles
  • only if they are at right angles to the line joining the particles
  • only if they are obliquely inclined to the line joining the particles
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