CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 5 - MCQExams.com

 Two masses of 1 gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is:
  • 4 : 1
  • 2 : 1
  • 1 : 2
  • 1 : 16
A sphere moving at some instant with horizontal velocity $$v_c $$ towards right and angular velocity in the anti-clockwise sense. If $$|v_c| = |\omega R|$$ The instantaneous center of rotation is:
  • at the bottom of the sphere
  • at the top of the sphere
  • at the centre of the sphere
  • Anywhere inside the sphere
Any point on the circumference of a rigid body which is rolling without slipping undergoes :
  • a circular path
  • an elleptic path
  • a cycloid path
  • an parabolic path
Rotation as well as translation motion is an example of
  • constrained motion
  • unconstrained motion
  • perpetual motion
  • None of these
$$ML^2T^{-2}$$ is the dimensional formula for
  • moment of inertia
  • pressure
  • elasticity
  • couple acting on a body
 Drum A undergoes
584209.JPG
  • rotational motion
  • translational motion
  • rotational as well as translational motion
  • None of these
Rolling without slipping is an example of
  • Rotation
  • Translation
  • Rotation with translation
  • None of these
Two bodies, $$A$$ and $$B$$ initially, at rest, move towards each other under mutual force of attraction. At the instant when the speed of $$A$$ is $$v$$ and that of $$B$$ is $$2v$$, the speed of the center of mass of the bodies is
  • $$3 v$$
  • $$2 v$$
  • $$1.5 v$$
  • Zero
The motion in which all points of a moving body move uniformly in the same line or direction is known as 
  • Rolling
  • Rotatory
  • Both A and B
  • Translational
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 of inertia of the molecule about an axis passing through the centre of mass and perpendicular to rod is :
  • Zero
  • $$(m_1+m_2)r^2$$
  • $$\dfrac{(m_1+m_2)}{m_1m_2}r^2$$
  • $$\left ( \dfrac{m_1m_2}{m_1+m_2} \right )r^2$$
Sagar was playing with the spinning top, after some time he realized that motion of top is same as motion of earth spinning about its own axis. Identify the type of motion?
  • Rotational motion
  • Oscillatory motion
  • Rectilinear motion
  • None of these
The radius of gyration of a disc of mass $$100 g$$ and radius $$5 cm$$ about an axis passing through its centre of gravity and perpendicular to the plane is (in cm)
  • $$0.5$$
  • $$2.5$$
  • $$3.54$$
  • $$6.54$$
Which of the following doesn't represent rotatory motion?
  • Both A and C
Let 'M' be the mass and 'L' be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is
  • $$1$$
  • $$\dfrac{1}{2}$$
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{8}$$
A body of mass $$m_{1} = 4\ kg$$ moves at $$5\hat {i}m/s$$ and another body of mass $$m_{2} = 2\ kg$$ moves at $$10\hat {i} m/s$$. The kinetic energy of centre of mass is :
  • $$\dfrac {200}{3}J$$
  • $$\dfrac {500}{3}J$$
  • $$\dfrac {400}{3}J$$
  • $$\dfrac {800}{3}J$$

Two particles A and B, initially at rest, moves towards each other under a mutual force of attraction. At the instant when the speed of A is $$u$$ and the speed of B is $$2 u$$, the speed of centre of mass is
  • Zero
  • $$u$$
  • $$1.5 u$$
  • $$3 u$$
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 center of mass of the system is
  • $$zero$$
  • $$v$$
  • $$1.5v$$
  • $$3v$$
Three identical thin rods, each of mass m and length l are joined to form an equilateral triangle. Find the moment of inertia of the triangle about one of its sides.
  • $$\displaystyle\frac{Ml^2}{2}$$
  • $$\displaystyle\frac{Ml^2}{3}$$
  • $$\displaystyle\frac{Ml^2}{9}$$
  • $$\displaystyle\frac{Ml^2}{12}$$
Two objects $$P$$ and $$Q$$ initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of $$P$$ is $$v$$ and that of $$Q$$ is $$2v$$, the velocity of centre of mass of the system is
  • $$v$$
  • $$3v$$
  • $$2v$$
  • $$1.5v$$
  • Zero
If a body of moment of inertia $$2$$kg $$m^2$$ revolves about its axis making $$2$$ rotations per school, then its angular momentum(in Js) is:
  • $$2\pi$$
  • $$4\pi$$
  • $$6\pi$$
  • $$8\pi$$
  • $$10\pi$$
A bicycle wheel rolls without slipping on a horizontal floor. Which one of the following is true about the motion of points on the rim of the wheel, relative to the axis at the wheel's centre?
741794_0037f17b75434bf4b4c7ee83f16bec59.png
  • Points near the top move faster than points near the bottom
  • Points near the bottom move faster than points near the top
  • All points on the rim move with the same speed
  • All points have the velocity vectors that are pointing in the radial direction towards the centre of the wheel
The radius of gyration of a solid cylinder of mass $$M$$ and radius $$R$$ about its own axis is
  • $$\dfrac { R }{ \sqrt { 2 } } $$
  • $$\dfrac { R }{ 2 } $$
  • $$\dfrac { R }{ \sqrt { 3 } } $$
  • $$\dfrac { R }{ 3 } $$
  • $$\dfrac { R }{ 4 } $$
State whether true or false :
The pendulum is said to be in mean position or stable equilibrium when the centre of mass of the bob lies directly below the the point of suspension.
  • True
  • False
A thin rod of length L is suspended from one end and rotated with n rotations per second. The rotational kinetic energy of the rod will be :
  • $$2mL^2\pi^2n^2$$
  • $$\frac{1}{2}mL^2\pi^2n^2$$
  • $$\frac{2}{3}mL^2\pi^2n^2$$
  • $$\frac{1}{6}mL^2\pi^2n^2$$
A rod of mass $$m$$ and length $$L$$, lying horizontally, is free to rotate about a vertical axis through its centre. A horizontal force of constant magnitude $$F$$ acts on the rod at a distance of $$L/4$$ from the centre. The force is always perpendicular to the rod. Find the angle rotated by the rod during the time $$t$$ after the motion starts.
  • $$\dfrac{3Ft^2}{5mL}$$
  • $$\dfrac{5Ft^2}{2mL}$$
  • $$\dfrac{3Ft^2}{2mL}$$
  • $$\dfrac{2Ft^2}{3mL}$$
Consider a ring rolling down a smooth inclined plane of vertical height 'h' and inclination $$\theta$$. Then the true statement in the following is?
  • Acceleration along the plane is g $$\sin\theta$$ and the potential energy at the topmost point is mgh
  • Acceleration along the plane is g and the potential energy at the top most point is mgh
  • Acceleration along the plane is g $$\sin\theta $$ and the potential energy at the top most point as mgh $$\sin\theta$$
  • None of these
Two bodies of mass $$10kg$$ and $$2kg$$ are moving with velocities $$2i-7j+3k$$ and $$-10i+35j-3k$$ $$m/s$$ respectively. The velocity of their CM is
  • $$2i$$ m/s
  • $$2k$$ m/s
  • $$(2i+2k)$$ m/s
  • $$(2i+2j+2k)$$ m/s
The radius of gyration of a solid sphere of radius $$R$$ about a certain axis is also equal to $$R$$. If $$r$$ is the distance between the axis and the centre of the sphere, then $$r$$ is equal to:
  • $$R$$
  • $$0.5R$$
  • $$\sqrt { 0.6 } R$$
  • $$\sqrt { 0.3 } R$$
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 speed of B is 2v, the speed of centre of mass of the system is :
  • zero
  • v
  • 1.5 v
  • 3 v
An automobile engine develops $$100$$ $$kW$$ when rotating at a speed of $$1800\ rev/min$$. The torque it delivers is
  • $$3.33\ N-m$$
  • $$200\ N-m$$
  • $$530.5\ N-m$$
  • $$2487\ N-m$$
A rigid body rotates about a fixed axis with variable angular velocity equal to (a-bt) at time t where a and b are constants. The angle through which it rotates before it comes to rest is___?
  • $$\dfrac{a^2}{b}$$
  • $$\dfrac{a^2}{2b}$$
  • $$\dfrac{a^2}{4b}$$
  • $$\dfrac{a^2}{2b^2}$$
A particle of mass $$m$$ describes a circle of radius $$r$$. The centripetal acceleration of the particle is $$\dfrac{4}{r^2}$$. Then the momentum of the particle is
  • $$2\dfrac {m}{r}$$
  • $$2\dfrac {m}{\sqrt {r}}$$
  • $$4\dfrac {m}{\sqrt {r}}$$
  • None of these
The centre of mass of a body :
  • lies always at the geometrical centre
  • lies always inside the body
  • lies always outside the body
  • may lie within or outside the body
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 system about one of the diagonals is:
  • $$\cfrac { 2M{ l }^{ 2 } }{ 3 } $$
  • $$\cfrac { 13M{ l }^{ 2 } }{ 3 } $$
  • $$\cfrac { M{ l }^{ 2 } }{ 6 } $$
  • $$\cfrac { 13M{ l }^{ 2 } }{ 6 } $$
The moment of inertia of a rod about its perpendicular bisector is I. When the temperature of the rod is increased by $$\triangle T$$, the increase in the moment of inertia of the rod about the same axis is (Here ,$$\alpha$$ is the coefficient of linear expansion of the rod)
  • $$\alpha I\triangle T$$
  • $$2\alpha I\triangle T$$
  • $$\dfrac{\alpha I \triangle T}{2}$$
  • $$\dfrac{2I\triangle T}{\alpha}$$
The moment of inertia of a solid sphere about an axis passing through the centre of gravity is $$1/2M{R}^{2}$$, then its radius of gyration about a parallel axis at a distance $$2R$$ from first axis is:
  • $$5R$$
  • $$\sqrt { \cfrac { 22 }{ 5 } } R$$
  • $$\cfrac { 5 }{ 2 } R\quad $$
  • $$\sqrt { \cfrac { 12 }{ 5 } } R$$
The cylinders P and Q are of equal of mas and length but made of metals with densities $${\rho _P}$$ and $${\rho _Q}\,\,\left( {{\rho _P} > {\rho _Q}} \right).$$ If their moment of inertia about an axis passing through centre and normal to the circular face be $${I_P}$$ and $${I_Q}$$, then:
  • $${I_P} = {I_Q}$$
  • $${I_P} > {I_Q}$$
  • $${I_P} < {I_Q}$$
  • $${I_P} \leqslant {I_Q}$$
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 system about an axis passing through the point of intersecion of diagonals and perpendicular to the plane of the square is:
  • $$\cfrac { 4M{ l }^{ 2 } }{ 3 } $$
  • $$\cfrac { 13M{ l }^{ 2 } }{ 3 } $$
  • $$\cfrac { M{ l }^{ 2 } }{ 6 } $$
  • $$\cfrac { 13M{ l }^{ 2 } }{ 6 } $$
The moment of inertia of a body rotating about a given axis is $$12.0 kg m^2$$ in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is $$5$$cm and the unit of mass is $$10g$$?
  • $$2.4 \times 10^3$$
  • $$6.0 \times 10^3$$
  • $$5.4 \times 10^3$$
  • $$4.8 \times 10^5$$
A ball of mass m moving with a constant velocity u strikes against a ball of same mass at rest. If e is the coefficient of restitution, then what will be the ration of velocity of two balls after collision?
  • $$\dfrac { 1-e }{ 1+e } $$
  • $$\dfrac { e-1 }{ e+1 } $$
  • $$\dfrac { 1+e }{ 1-e } $$
  • $$\dfrac { e+1 }{ e-1 } $$
The radius of gyration of a ring of mass 80 g and diameter 6 cm, about an axis passing through its center of gravity and perpendicular to the plane is:
  • 3 cm
  • 6 cm
  • 9 cm
  • 4 cm
Two particles of mass $$1\ kg$$ and $$3\ kg$$ move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is $$2\ m/s$$, their centre of mass has a velocity of $$0.5\ m/s$$, then the velocity of the centre of mass is $$0.75\ m/s$$.
  • True
  • False
The figure below shows a pattern of two fishes. Write the mapping rule for the rotation of Image A to Image B.
 
1002237_cf661886db494aec916c98bc42d7fb7f.PNG
  • Image B has to be rotated by 90 degrees anticlockwise to map with image A
  • Image B should first have a mirror reflection and then be rotated to map with image A
  • The width of image B should be reduced by 1 unit (1 square in the graph shown) and then rotated by 90 degrees to map with image A
  • The width of image B should be increased by 1 unit (1 square in the graph shown) and then rotated by 90 degrees to map with image A
A long slender rod of mass $$2\ kg$$ and length $$4\ m$$ is placed on a smooth horizontal table. Two particles of masses $$2\ kg$$ and $$1\ kg$$ strike the rod simultaneously and stick to the rod after collision as shown in Figure.
Velocity of the centre of mass of the rod after collision is
985887_e399cde2eb8e4397b8430f2667c146d1.jpg
  • $$12\ m/s$$
  • $$9\ m/s$$
  • $$6\ m/s$$
  • $$3\ m/s$$
A string is wrapped around a cylinder of mass $$M$$ and radius $$R$$. The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string, The work done on the cylinder for reaching an angular speed $$\omega$$ is:
  • $$\cfrac { 2M{ R }^{ 2 }{ \omega }^{ 2 } }{ 3 } $$
  • $$\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 3 } $$
  • $$\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 2 } $$
  • $$\cfrac { M{ R }^{ 2 }{ \omega }^{ 2 } }{ 4 } $$
Three particles of equal masses are placed at the corners of an equilateral triangle as shown in the figure. Now particle A starts with a velocity $$\nu_1$$ towards line $$AB$$, particle $$B$$ starts with a velocity $$\nu_2$$ towards line $$BC$$ and particle $$C$$ starts with velocity $$\nu_3$$ towards line $$CA$$. The displacement of $$CM$$ of three particle A, B and C after time $$t$$ will be (given if $$\nu_1 = \nu_2 = \nu_3$$)
1002649_ed4fc121e1b6486dac642a923ec91234.png
  • zero
  • $$\dfrac{\nu_1 + \nu_2 + \nu_3}{3}t$$
  • $$\dfrac{\nu_1 + \dfrac{\sqrt{3}}{2}\nu_2 + \dfrac{\nu_3}{2}}{3}t$$
  • $$\dfrac{\nu_1 + \nu_2 + \nu_3}{4}t$$
If a car is moving forward, what is the direction of the moment of the moment caused by the rotation of the tires
  • It is heading inwards, i.e. the direction is towards inside of the car
  • It is heading outwards, i.e. the direction is towards outside of the car
  • It is heading forward, i.e. the direction is towards the forward direction of the motion of the car
  • It is heading backward, i.e. the direction is towards back side of the motion of the car
A gun of mass $$M$$, frees a shell of mass $$m$$ horizontally and the energy of explosion is such as would be sufficient to project the shell vertically to a height '$$h$$'. The recoil velocity of the gun is:
  • $$\left(\dfrac{2m^2gh}{M(m + M)}\right)^{\dfrac{1}{2}}$$
  • $$\left(\dfrac{2m^2gh}{M(m - M)}\right)^{\dfrac{1}{2}}$$
  • $$\left(\dfrac{2m^2gh}{2M(m - M)}\right)^{\dfrac{1}{2}}$$
  • $$\left(\dfrac{2m^2gh}{2M(m + M)}\right)^{\dfrac{1}{2}}$$
Four particles of equal masses are placed on the vertices of a square and are rotated with a uniform angular velocity about one of the edges (A) as shown in the figure. Which particle will have a larger angular momentum
1003078_2cb3ea717a044c29b03ccf0e33e2ea5b.png
  • A
  • B
  • C
  • D
The ratio of the radii of gyration of a hollow sphere and a solid sphere of the same masses and radii about an axis passing through their centre is 
  • $$\sqrt{2/3}$$
  • $$\sqrt{2/5}$$
  • $$\sqrt{5/3}$$
  • $$\sqrt{5/2}$$
0:0:1


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