CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 10 - MCQExams.com

The velocity of centre of mass of the system as shown in the figure.
1433430_ca2fa8773b6648218d993797951ddef7.png
  • $${(\dfrac{2-2\sqrt{3}}{3})}\hat{i}-\dfrac{1}{3} \hat{j}$$
  • $${(\dfrac{2+2\sqrt{3}}{3})}\hat{i}-\dfrac{2}{3} \hat{j}$$
  • $$4\hat{i}$$
  • None of these
The M.I of a thin rod of length $$l$$ 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-
  • $$\dfrac{4}{3}I$$
  • $$\dfrac{8}{3}I$$
  • $$\dfrac{1}{2}I$$
  • $$16I$$
A uniform rod of mass $$m$$ and length $$l$$ hinged at its end is released from rest when  it is in the horizontal position. The normal reaction at the hinged when the rod becomes vertical is
  • $$\cfrac {mg}4$$
  • $$\cfrac 5 2 mg$$
  • $$\cfrac {mg} 6$$
  • $$\cfrac 72 mg$$
If the kinetic energy of a body is increased by 300% then determine the percentage increase in the  momentum 
  • 100 %
  • 150 %
  • $$ \sqrt {300%} $$
  • 175 %
The moment of inertia of a uniform thin rod of length $$L$$ and mass $$M$$ about an axis passing through a point at a distance of $$\cfrac{L}{3}$$ from one of its ends and perpendicular to the rod is
  • $$\cfrac{7M{L}^{2}}{48}$$
  • $$\cfrac{M{L}^{2}}{9}$$
  • $$\cfrac{M{L}^{2}}{12}$$
  • $$\cfrac{M{L}^{2}}{3}$$
A rod of moment of inertia I and length L is suspended from a fixed end and given small oscillations about the point of suspension , the restoring torque is found to be -(mgL/2) $$sin\theta $$ What will be the angular equation of motion of the SHM
  • $$\dfrac { { d }^{ 2 }\theta }{ { dt }^{ 2 } } +\left( mgL/I \right) \theta =0$$
  • $$\dfrac { { d }^{ 2 }\theta }{ { dt }^{ 2 } } +\left( mgL/2I \right) \theta =0$$
  • $$\dfrac { { d }^{ 2 }\theta }{ { dt }^{ 2 } } +\left( 2mgL/I \right) \theta =0$$
  • $$\dfrac { { d }^{ 2 }\theta }{ { dt }^{ 2 } } +\left( mgL/4I \right) \theta =0$$
If a square of side $$R/2$$ is removed from a uniform circular disc of radius $$R$$ as shown in the figure, the shift in centre of mass is
  • $$\dfrac{R}{4 \pi - 1}$$
  • $$\dfrac{R}{2(4 \pi - 1)}$$
  • $$\dfrac{R}{3(4 \pi - 1)}$$
  • $$\dfrac{R}{4(4 \pi - 1)}$$
The moment of inertia of a metre scale of mass 0.6 kg about an axis perpendicular to the scale and located at the 20 cm position on the scale in kg $$m^2$$ is (Breadth of the scale is negligible)
  • 0.074
  • 0.104
  • 0.148
  • 0.208
Three identical rods, each of length I, are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is
  • $$\dfrac { \ell }{ \sqrt { 3 } } $$
  • $$\dfrac { \ell }{ \sqrt { 2 } } $$
  • $$\dfrac { \ell }{ \sqrt { 5 } } $$
  • $$\dfrac { \ell }{ \sqrt { 7 } } $$
Force F=300 N acting vertically upward at x=2 m, y=2 m. The magnitude of moment of force about origin is
  • 600 Nm
  • 660 Nm
  • 300 Nm
  • 330 Nm
A solid cylinder of mass  $$500 \mathrm{g}  $$ and radius $$10  \mathrm{cm}  $$ .has radius of gyration about the axis $$  y y' $$ as given below is
1504349_7d88ea8974e440b693b2e8bc352ca23a.png
  •  $$10 \sqrt{2} \mathrm{cm} $$
  •  $$ \dfrac{10}{\sqrt{2}} \mathrm{cm} $$
  •  $$5 \sqrt{2} \mathrm{cm} $$
  • $$ \frac{5}{\sqrt{2}} \mathrm{cm} $$
Two identical uniform rod each of mass $$m$$ and length $$l$$ joined perpendicular to each other. An axis passes through junction and in the plane of rods. Then $$M.I.$$ of system about the axis is 
1576967_1d5e8fca48a34fb5b9c8be3b77668248.png
  • $$\dfrac{1}{3} ml^2$$
  • $$\dfrac{1}{3\sqrt{2}} ml^2$$
  • $$ ml^2$$
  • $$\dfrac{ml^2}{2}$$
The temperature of a thin uniform rod increase by $$\Delta t$$ If moment of intertia 1 about an axis perpendicular to its length then its moment of increase by 
  • 0
  • $$\alpha I\Delta t$$
  • $$2\alpha I\Delta t$$
  • $${ \alpha }^{ 2 }I\Delta t$$
Ratio of radii of gyration of a hollow & solid sphere of the same radii about the axis which is tangent to the sphere is 
  • $$\sqrt { \dfrac73 } $$
  • $$\dfrac {5}{\sqrt {21}} $$
  • $$\sqrt { \dfrac { 4 }{ 5 } } $$
  • $$\dfrac{25}9$$
A shown in figure two uniform rods of mass M and length L each are joined . what is the moment of inertia of system about an axis perpendicular to plane through end A?
1577168_c187903009424a948026cc493817c820.png
  • $$ \frac { 5ML^2}{3} $$
  • $$ \frac { 7ML^2}{3} $$
  • $$ \frac { 5ML^2}{12} $$
  • $$ \frac { 7ML^2}{12} $$
If moment of inertia of a point particle at a distance r from an axis would have defined as $$L = mr$$ instead of L=$${ mr }^{ 2 }$$, then moment of inertia of a uniform rod of mass M and length L about an axis passing through centre of mass and perpendicular to the rod will be (moment of inertia is still a scalar ) 
  • $$\dfrac { ML }{ 12 } $$
  • $$\dfrac { { ML }^{ 2 } }{ 12 } $$
  • $$\dfrac { ML }{ 4 } $$
  • Zero
Three identical uniform rods each of length 1 m and mass 2 kg are arranged to form an equilateral triangle. What is the moment of inertia of the system about an axis passing through one corner ans perpendicular to the plane of the triangle:-
  • $$4 kg-{ m }^{ 2 }$$
  • $$3 kg-{ m }^{ 2 }$$
  • $$2 kg-{ m }^{ 2 }$$
  • $$5 kg-{ m }^{ 2 }$$
The moment of inertia of uniform thin rod of mass m and length l about two axis PQ and RS passing through centre of rod C and in the plane of the rod are $$ I_{PQ} and I_{RS} $$ respectively. then $$ I_{PQ}+I_{RS}$$ is equal to
1568591_477252e752cf471494a7d85210baf052.PNG
  • $$ \frac {ml^2}{3} $$
  • $$ \frac {ml^2}{2} $$
  • $$ \frac {ml^2}{4} $$
  • $$ \frac {ml^2}{12} $$
A point at which a whole weight of body act vertically downward is ________.
  • centre of gravity
  • centre of mass
  • centre of force
  • centre of acceleration
A uniform rod of mass $$m$$ is bent into the form of a semicircle of radius $$R$$. The moment of inertia of the rod about an axis passing through $$A$$ and perpendicular to the plane of the paper is 
  • $$mR^2$$
  • $$mR$$
  • $$3mR$$
  • $$2mR$$
Two  particles which are initially at  rest, move towards  each other  under the action of  their intrnal attraction.  If  their speeds are V and 2V at any instant, then the speed of centre of mass of the system will be 
  • $$V$$
  • $$2V$$
  • $$Zero$$
  • $$1.5V$$
Two particle of masses $$ m_1 and   m_2 $$ initially at rest start moving towards each other under their mutual force of attraction, The speed of the center of mass at any time t, when they are at distance r apart , is
  • zero
  • $$ \left( G\frac { m_{ 1 }m_{ 2 } }{ r^{ 2 } } ,\frac { 1 }{ \quad m_{ 1 } } \right) t $$
  • $$ \left( G\frac { m_{ 1 }m_{ 2 } }{ r^{ 2 } } ,\frac { 1 }{ \quad m_{ 2 } } \right) t $$
  • $$ \left( G\frac { m_ 1m_ 2 }{ r^ 2 } ,\frac { 1 }{ m_ 1\quad +\quad m_ 2 } \right) t $$
The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius $$R$$, (ii) a solid cylinder of radius $$\cfrac{R}{2}$$ and (iii) a solid sphere of radius $$\cfrac{R}{4}$$. If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:
  • $$4:3:2$$
  • $$14:15:20$$
  • $$10:15:7$$
  • $$2:3:4$$
A solid sphere of radius $$R$$ has total charge $$2Q$$ and volume charge density $$\rho = kr$$ where $$r$$ is distance from centre. Now charges $$Q$$ and $$-Q$$ are placed diametrically opposite at distance $$2a$$ where $$a$$ is distance form centre of sphere such that net force on charge $$Q$$ is zero then relation between $$a$$ and $$R$$ is
  • $$a = R/2$$
  • $$a = R$$
  • $$a = 2R$$
  • $$a = 3R/4$$
Two forces, each of magnitude $$F$$, act at points $$V$$ and $$W$$ on an object.
The two forces form a couple. The shape of the object is a right-angled triangle with sides of
lengths $$x$$ and $$y$$, as shown.
Which expression gives the torque exerted by the couple?

1648473_6fef94a757b44fc88c579cedec7e1712.png
  • $$Fx$$
  • $$Fy$$
  • $$2Fx$$
  • $$2Fy$$
Two particles $$A$$ and $$B$$ of equal masses have velocities $$v_A = 2i + j$$ and $$v_B = - i + 2j$$. The particles move with accelerations $$a_A  = - 4i- j$$ and $$a_B = - 2i + 3j$$ respectively. The centre of mass of the two particles move along 
  • A straight line
  • a parabola
  • a circle
  • an ellipse LINE
A wooden plank rests in equilibrium on two rocks on opposite sides of a narrow stream. Three forces P, Q and R act on the plank. How are the sizes of the forces related?
1645208_37b44c17620146e5b9d4eafadb731381.png
  • P$$+$$Q$$=$$R
  • P$$+$$R$$=$$Q
  • P$$=$$Q$$=$$R
  • P$$=$$Q$$+$$R
Distance  of  the centre of mass of a solid uniform cone from its  vertex is $$Z_{0}$$  If  the radius  and its height is h then $$Z_{0}$$  is equal to 
  • $$\dfrac{h^{2}}{4R}$$
  • $$\dfrac{3h}{4}$$
  • $$\dfrac{5h}{8}$$
  • $$\dfrac{3h^{r}}{8R}$$
Water is drawn from a well in a $$5\ kg$$ drum of capacity $$55\ L$$ by two ropes connected to the top of the drum. The linear mass density of each rope is $$0.5\ kgm^{-1}$$. The work done in lifting water to the ground from the surface of water in the well $$20\ m$$ below is $$[g=10\ ms^{-2}]$$
  • $$1.4\times 10^{4}\ J$$
  • $$1.5\times 10^{4}\ J$$
  • $$9.8\times 10\times 6\ J$$
  • $$18\ J$$
A uniform rod of length of $$1$$m and mass of $$2$$kg is attached to a side support at $$0$$ as shown in the figure. The rod is at equilibrium due to upward force T acting at P. Assume the acceleration due to gravity as $$10m/s^2$$. The value of T is?
1698596_29b73cbe9adb446f8f9d3654b86ac315.png
  • $$0$$
  • $$2$$N
  • $$5$$N
  • $$10$$N
  • $$20$$N
Find the velocity of centre of mass of the system shown in the figure
1702133_2846b0ea5d6845e39ee5b6b8c4db6bc1.png
  • $$\left(\dfrac{2+2\sqrt{3}}{3}\right)\hat{i}-\dfrac{2}{3}\hat{j}$$
  • $$4\hat{i}$$
  • $$\left(\dfrac{2-2\sqrt{3}}{3}\right)\hat{i}-\dfrac{1}{3}\hat{j}$$
  • $$None\ of\ these$$
A block of mass $$m$$ having coefficient of friction $$\mu$$ with the floor $$F$$ is placed at one end of the spring. The spring is attached to this block and a vertical shafts. The floor with the shaft is given an angular acceleration $$\alpha$$ Then:
1702143_cf5b3fc743c5439c90a0f42931742cfd.png
  • The spring cannot elongate before $$t=\dfrac {\sqrt {\mu g}}{l \alpha^2}$$
  • The spring elongates as soon as the rotation starts
  • The stored energy in the spring goes on increasing right from $$t=0$$ onwards
  • The maximum spring force acts at $$t=\dfrac {\sqrt {\mu g}}{l \alpha^2}$$
Mark correct option or options:
  • Nagpur can be said to the geographical centre of India
  • The population centre of India may be Uttar Pradesh
  • The population centre may be coincided with geographical centre
  • All the above
In which of the following cases the centre of mass of a rod is certainly not at its geometrical centre?
  • The density continuously decreases from left to right
  • The density continuously increases from left to right
  • The density decreases from left to right upto the centre and then increases
  • Both $$(a)$$ and $$(b)$$ are correct
A cracker is thrown into air with a velocity of $$10$$ m/s at an angle of $$45^o$$ with the vertical. When it is at a height of $$0.5$$m from the ground, it explodes into a number of pieces which follow different parabolic paths. What is the velocity of centre of mass, when it is at a height of $$1$$m from the ground? ($$g=10m/s^2$$)
  • $$4\sqrt{5}$$ m/s
  • $$2\sqrt{5}$$ m/s
  • $$5\sqrt{4}$$ m/s
  • $$10$$ m/s
A rigid body is in pure rotation , that is undergoing fixed axis rotation. then which of the following statements are true ?
  • You can find two points in the body in a plane perpendicular to the axis of rotation having the same velocity
  • You can find two points in the body in a plane perpendicular to the axis of rotation having the same acceleration.
  • Speed of all the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is the same
  • Angular speed of the body is the same seen from any point in the body
The mathematical statement $$\vec{v}=\vec{v_c}+\vec{v'}$$, where $$\vec{v_c}$$ is the velocity of centre of mass, $$\vec{v'}$$ is the velocity of the point with respect to the centre of mass and $$\vec{v}$$ is the total velocity of the point with respect to the ground.
  • Is true for a rolling sphere
  • Is true for a block moving on a frictionless horizontal surface
  • Is true for a rolling cylinder
  • None of these
A ball falls vertically onto a floor with momentum p, and then bounces repeatedly. If the coefficient of restitution is e, then the total momentum impareted by the ball on the floor till the ball comes to rest is?
  • $$p(1+e)$$
  • $$\dfrac{p}{1-e}$$
  • $$p\left(1+\dfrac{1}{e}\right)$$
  • $$p\left(\dfrac{1+e}{1-e}\right)$$
Which of the following statements are correct for instantaneous axis of rotation?
  • Acceleration of every point lying on the axis must be equal to zero.
  • velocity of a point at a distance r from the axis is equal to $$ r \omega $$
  • if moment of inertia of a body about the axis is I and angular velocity is $$ \omega $$ then kinetic energy of the body is equal $$ I \omega^2 / 2$$
  • Moment of inertia of a body is least about instantaneous axis of rotation among all the parallel axes.
Three-point masses $$ m_1, m_2\ and\ m_3 $$ are located at the vertices of an equilateral triangle of side $$ á'$$ what is the moment of inertia of the system about an axis along the altitude of the triangle passing through $$ m_1 $$?
  • $$ (m_1 +m_2) \dfrac {a^2}{4} $$
  • $$ ( m_2 +m_2) \dfrac {a^2}{4} $$
  • $$ ( m_1+ m_3) \dfrac {a^2}{4} $$
  • $$ (m_1+ m_2 + m_3) \dfrac {a^2}{4} $$
A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass.
  • Of the box remains constant
  • Of the (box $$+$$ ball) system remains constant
  • Of the ball remains constant
  • Of the ball relative to the box remains constant
A train of mass M is moving on a circular track of radius 'R' with constant speed V. The length of the train is half of the perimeter of the track. The linear momentum of the train will be?
  • $$0$$
  • $$\dfrac{2MV}{\pi}$$
  • $$MVR$$
  • $$MV$$
The graph between kinetic energy and momentum of a particle is plotted as shown in Fig. The mass of the moving particle is?
1735375_df4583c00ee4478a96aa10a446efa387.PNG
  • $$1$$ kg
  • $$2$$ kg
  • $$3$$ kg
  • $$4$$ kg
Two identical rods are joined to form an $$'X'$$. The smaller angle between the rods is $$\theta$$. The moment of inertia of the system about an axis passing through point of intersection of the rods and perpendicular to their plane is proportional to :
  • $$\theta$$
  • $$\sin^2 \theta$$
  • $$\cos^2 \theta$$
  • independent of $$\theta$$
Distance moved by cylinder during time taken by it to complete one rotation is:
  • $$2\pi R$$
  • $$\pi R$$
  • $$3\pi R$$
  • $$\dfrac{4\pi R}{3}$$
Two particles A and B, initially at rest, move towards each other  under a mutual force of attraction. At the instant when the speed of A is V and the speed of B is 2V, the speed of the centre of mass of the system is 
  • 3V
  • V
  • 1.5 V
  • Zero
Distance moved by hanging mass during the above time interval is :
  • $$2\pi R$$
  • $$\pi R$$
  • $$3\pi R$$
  • $$\dfrac{4\pi R}{3}$$
Velocity of the center of mass of the rod after collision is 
  • 12 m/s
  • 9 m/s
  • 6 m/s
  • 3 m/s
Acceleration of cylinder is :
  • $$g$$
  • $$\dfrac{g}{2}$$
  • $$\dfrac{g}{4}$$
  • $$\dfrac{3g}{4}$$
A wire of length $$l$$ and mass $$m$$ is first bent into a circle, then in a square and then in an equilateral triangle. The moment of inertia in these three cases about an axis perpendicular to their planes and passing through their centers of masses are $$I_1$$  $$I_{2}$$ & $$I_{3}$$ respectively. Then maximum of them is:
  • $$I_{1}$$
  • $$I_{2}$$
  • $$I_{3}$$
  • data insufficient
0:0:1


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