CBSE Questions for Class 11 Engineering Physics Systems Of Particles And Rotational Motion Quiz 3 - MCQExams.com

The momentum of a system is defined
  • As the product of mass of the system and the velocity of centre of mass
  • As the vector sum of the momentum of individual particles
  • For bodies undergoing translational, rotational and oscillatory motion
  • All of the above
Which of the following is/are the properties of moment of a couple?
  • It tends to produce pure rotation.
  • It is different about any point in the plane of lines of action of the forces.
  • It can be replaced by any other couple of the same moment.
  • The resultant of set of two or more couples is equal to the sum of the moments of the individual couples.
The momentum of a system with respect to centre of mass-
  • Is zero only if the system is moving uniformly.
  • Is zero only if no external force acts on the system.
  • Is always zero.
  • Can be zero in certain conditions.
A couple can never be replaced by a single force.
  • True
  • False
The point through which the total weight appears to act for any orientation of the object is ______.
  • centre of gravity.
  • centre of momentum
  • centre of force
  • none of the above
The diameter of a solid disc is $$0.5m$$ and its mass is $$16kg$$.
What torque is required to increase its angular velocity about an axis perpendicular to its plane from zero to $$120$$ rotations/minute in $$8$$ seconds?
  • $$\cfrac { \pi }{ 4 } N/m$$
  • $$\cfrac { \pi }{ 2 } N/m$$
  • $$\pi N/m$$
  • $$2\pi N/m$$
The center of mass of a system of particle is at the origin. it follows that :
  • the number of particles to the right of the origin is equal to the number of particles to left.
  • the total mass of the particles to the right of the origin is same as the total to the left of the origin.
  • the number of particles on X-axis should be equal to the number of particles on Y-axis.
  • if there is a particle on the X-axis, there must be at least one particle on the negative X-axis.
  • none
A ball kept in a closed container moves in it making collision with the walls. The container is kept on a smooth surface. The velocity of the centre of mass of :
  • the ball remains fixed
  • the ball relative to container remains fixed.
  • the container remains fixed
  • both container and ball remain fixed.
A body having it's center of mass  at the origin. Then,
(The question having a multiple answers).
  • x co-ordinates of the particles may be all positive.
  • total KE must be conserved.
  • total KE must very.
  • total momentum shall vary.
A car sometimes overturns while taking a turn. When it overturns, :
  • the inner wheel leaves the ground first.
  • the outer wheel leaves ground first.
  • both the wheels leave the ground simultaneously.
  • either of the wheels leaves the ground first.
A ladder is leaned against a smooth wall and allowed to slip on a frictionless floor. Which figure represents trace of its COM ?
A body has its center of mass at the origin. The x-axis coordinates of the particles :
  • may be all positive
  • may be all negative
  • should be all at zero
  • may be positive for some case and negative in other cases.
A particle of mass m is moving in horizontal circle of radius $$r$$ with uniform speed $$v$$. When it  moves from one point to a diametrically opposite point its 
  • KE changes by $$mv^2$$.
  • KE changes by $$\dfrac{1}{4}mv^2$$.
  • momentum does not change.
  • momentum changes by $$2 mv$$.
Two balls of equal masses are projected upward simultaneously, one from the ground with speed $$50m/s$$ and other from a $$40m$$ high tower with initial speed $$30m/s$$. Find the maximum height attained by their centre of mass.
  • 100 m
  • 200 m
  • 150 m
  • 50 m
A pulley is hinged at the centre and a massless thread is wrapped around it. The thread is pulled with a constant force F starting from rest. As the time increases:
125877_3e4ad5f78de84926bd41c11ac8650d16.png
  • its angular velocity increases, but force on hinge remains constant.
  • its angular velocity remains same, but force on hinge increases.
  • its angular velocity increases and force on hinge increases.
  • its angular velocity remains same and force on hinge is constant.
A particle of mass $$m$$ strikes a wall with a velocity $$v$$ making an angle $$\theta$$ with the wall and rebounds.The change in momentum of the particle will be :
  • $$-2m\overline{v} cos \theta$$
  • $$0$$
  • $$2m\overline{v}$$
  • $$-2m\overline{v} sin \theta$$

Which of the following statement is correct for instantaneous axis of rotation?
  • Acceleration of every point lying on the axis must be equal to zero
  • Velocity of a point distance $$r$$ from the axis is equal to $$r\omega$$
  • If moment of inertia of the body about the axis be I and angular velocity be $$\omega$$ then total kinetic energy of all body is equal to $$\displaystyle{\frac{1}{2}I\omega^2}$$
  • Moment of inertia of a body is least about instantaneous axis of rotation among all the parallel axis

Two identical rods are joined to form the shape of X. the smaller angle between rods is $$\theta$$. The moment of inertia of the system about an axis passing through the point of intersection of the rod and perpendicular to their plane is
  • $$I \propto \theta$$
  • $$I \propto sin^2\theta$$
  • $$I\propto cos^2 \theta$$
  • Independent of $$\theta$$

Which of the following is not correct about centre of mass ?
  • It depends on the choice of frame of reference
  • In centre of mass frame, momentum of a system is always zero
  • Internal forces may affect the motion of centre of mass
  • Centre of mass and centre of gravity coincide in uniform gravitational field
Four identical rods, each of mass $$m$$ and length $$l$$, are joined to form a rigid square frame. The frame lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its moment of inertia about :
  • the x-axis is $$\displaystyle \frac{2}{3} \, ml^2$$
  • the z-axis is $$\displaystyle \frac{4}{3} \, ml^2$$
  • an axis parallel to the z-axis and passing through a corner is $$\displaystyle \frac{10}{3} \, ml^2$$
  • one side is $$\displaystyle \frac{5}{2} \, ml^2$$

Two particles of mass 1 kg and 3 kg move towards each other under mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is $$\displaystyle{2 ms^{-1}}$$ their centre of mass has a velocity of $$\displaystyle{0.5 ms^{-1}}$$ and when their velocity of approach become $$\displaystyle{3 ms^{-1}}$$, the velocity of their centre of mass is $$\displaystyle{0.75 ms^{-1}}$$. Then,
  • Above statement is correct
  • Above statement is false
  • Above statement may be correct or incorrect
  • Velocity of centre of mass can change in the given case
Find the acceleration of the point $$K$$.
141860_a11146ca4d2342939331d84ff652b2f6.png
  • $$\displaystyle w=\frac{F(3m_1+2m_2)}{m_1(m_1+m_2)}$$
  • $$\displaystyle w=\frac{F(3m_1+m_2)}{m_1(m_1+m_2)}$$
  • $$\displaystyle w=\frac{F(m_1+m_2)}{m_1(m_1+m_2)}$$
  • $$\displaystyle w=\frac{F(m_1+2m_2)}{m_1(m_1+m_2)}$$
A particle of rest mass $$m_0$$ is moving with speed $$c/2$$. What is its momentum? 
  • $$\displaystyle \frac{m_0c}{2}$$
  • $$\displaystyle \frac{1}{\sqrt{3}}m_0c$$
  • $$\displaystyle \frac{2}{\sqrt{3}}m_0c$$
  • none of the above

For a rigid body made up of N particles each of mass m, the radius of gyration, about a given axis of rotation, equals to the
  • Distance of any constituent particles from the axis of rotation
  • Mean of the distance of the constituent particles from axis of rotation
  • Root mean square value of the distance of the constituent particle from axis if rotation
  • Harmonic mean of the distance of the constituent particles from the axis of rotation

The distance of the centre of mass of the T-shaped plate from O is


149257.png
  • 7 m
  • 2.7 m
  • 4 m
  • 1.7 m
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? $$(g = 10 m/s^2)$$
  • $$4 \sqrt{5} m/s$$
  • $$2 \sqrt{5} m/s$$
  • $$4 \sqrt{4} m/s$$
  • 10 m/s
A particle of mass $$m$$ is acted on by two forces of equal magnitude $$F$$ maintaining their orientation relative to the velocity $$v$$ as shown in figure. The momentum of the particle :
157120_940ba90dd560474eb24cecdfcd46c09f.png
  • increases in (a)
  • decreases in (b)
  • only the direction changes in (c)
  • All of the above
Two particles are shown in figure. At $$t = 0$$, a constant force $$F = 6$$N starts acting on the 3 kg mass. Find the velocity of the centre of mass of these particles at $$t = 5 s$$.
156802_ee4e52c6aac84434ad3c8a52767a20f5.png
  • $$5 m/s$$
  • $$4 m/s$$
  • $$6 m/s$$
  • $$3 m/s$$
The moment of inertia of a solid sphere about an axis passing through the centre of gravity is $$2/5 MR^{2}$$, then its radius of gyration about a parallel axis at a distance $$2R$$ from first axis is 
  • $$5R$$
  • $$\displaystyle\ \sqrt{\frac{22}{5}} R$$
  • $$\displaystyle\ \frac{5}{2} R$$
  • $$\displaystyle\ \sqrt{\frac{12}{5}}R$$
For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of body?
  • a ring of radius $$l$$
  • a disc of radius $$l$$
  • a square lamina of side $$2l$$
  • four rods forming square of side $$2l$$
Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks in the centre of mass frame after the kick are, respectively :
  • 4 m/s, 4 m/s
  • 10 m/s, 4 m/s
  • 4 m/s, 10 m/s
  • 10 m/s, 10 m/s
Four identical rods each of mass $$M$$ are joined to form as square frame. The moment of inertia of the system about an axis passing through the point of intersection of diagonals and perpendicular to the plane of the square is 
  • $$\displaystyle\ \frac{4Ml^{2}}{3}$$
  • $$\displaystyle\ \frac{13Ml^{2}}{3}$$
  • $$\displaystyle\ \frac{Ml^{2}}{6}$$
  • $$\displaystyle\ \frac{13Ml^{2}}{6}$$
A man stands at one end of the open truck which can run on frictionless horizontal rails. Initially, the man and the truck are at rest. Man now walks to the other end and stops. Then which of the following is true?
  • The truck moves opposite to direction of motion of the man even after the man ceases to walk.
  • The centre of mass of the man and the truck remains at the same point throughout the man's walk.
  • The kinetic energy of the man and the truck are exactly equal throughout the man's walk.
  • The truck does not move at all during the man's walk.
Four identical rods each of mass $$M$$ are joined to form as square frame, the moment of inertia of the system about one of the diagonals is 
  • $$\displaystyle\ \frac{13Ml^{2}}{3}$$
  • $$\displaystyle\ \frac{2Ml^{2}}{3}$$
  • $$\displaystyle\ \frac{Ml^{2}}{6}$$
  • $$\displaystyle\ \frac{13Ml^{2}}{6}$$
How can be rule be brought in equilibrium by using an additional weight of $$40gf$$?

185048_1a218293fc5548938d33d4e8174dbdfe.png
  • By placing the additional weight of $$80gf$$ at the $$30cm$$ mark.
  • By placing the additional weight of $$80gf$$ at the $$70cm$$ mark.
  • By placing the additional weight of $$40gf$$ at the $$30cm$$ mark.
  • By placing the additional weight of $$40gf$$ at the $$70cm$$ mark.
The horizontal beam in figure weights $$150 N$$, and its centre of gravity is at its centre. Find the tension in the cable.
158796_221076d084f84a7b8777d0b74fd4dc47.png
  • $$75 N$$
  • $$500 N$$
  • $$300 N$$
  • $$625 N$$
In situation (i), just after both A and B jump from the platform, velocity of centre of mass of the system (A, B and the platform) is :
  • 2 m/s
  • 6 m/s
  • 5 m/s
  • none of these
Two particles A and B initially at rest, move towards each other by mutual force of attraction. At the instant when the speed of A is n and the speed of B is 3n, the speed of the centre of mass of the system is :
  • 3n
  • 2n
  • 1.5n
  • 0
A particle having mass $$0.5\ kg$$ is projected under gravity with a speed of $$98\  m/sec$$ at an angle of $$60^{\circ} $$.The magnitude of the change in momentum $$($$in N sec$$)$$ of particle after  $$10\  seconds$$ is :
  • $$0.5$$
  • $$49$$
  • $$98$$
  • $$490$$
A thin uniform circular ring is rolling down an inclined plane of inclination $$30^{\small\circ}$$ without slipping. Its linear acceleration along the inclined plane will be
  • $$g/2$$
  • $$g/3$$
  • $$g/4$$
  • $$2g/3$$
A couple produces
  • Linear motion
  • Rotational motion
  • Both $$A$$ and $$B$$
  • Nether $$A$$ nor $$B$$
A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by $$\mbox{1 %}$$. Its angular speed will
  • Increase approximately by $$\mbox{1 %}$$
  • Decrease approximately by $$\mbox{1 %}$$
  • Decrease approximately by $$\mbox{0.67 %}$$
  • Decrease approximately by $$\mbox{0.33 %}$$
A projectile of mass $$m$$ is thrown with velocity $$v$$ making an angle $$ 60^{\circ} $$ with the horizontal. Neglecting air resistance, the change in momentum from the departure A to its arrival at B, along the vertical direction is :
184032.png
  • $$2 mv $$
  • $$\sqrt{3} mv $$
  • $$ mv $$
  • $$\dfrac{mv}{\sqrt{3}} $$

217292_7d3960818eef465c81d2a27315454b13.png
  • If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
  • If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
  • If Assertion is true, but the Reason is false.
  • If Assertion is false but the Reason is true

217295_94c22bfe04c44557a880a0c2cc826b66.png
  • If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
  • If both Assertion and Reason are tl1le but Reason is not the correct explanation of Assertion
  • If Assertion is true, but the Reason is false.
  • If Assertion is false but the Reason is true
The radius of gyration of a disc of radius 25 cm about an axis passing through the center of the disc and perpendicular to the disc is approximately equal to:
  • $$17.7 cm$$
  • $$12.5cm$$
  • $$36cm$$
  • $$50cm$$
Statement 1: When we lean behind over the hind legs of the chair, the chair falls back after a certain angle.

Statement 2: Centre of mass lying outside the system makes the system unstable.
  • Statement 1 is false, Statement 2 is true
  • Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1
  • Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1
  • Statement 1 is true, Statement 2 is false
A projectile of mass $$m$$ is fired with velocity $$v$$ from a point as shown in figure, neglecting air resistance, what is the change in momentum when leaving $$P$$ and arriving at $$Q$$ ?


279964_1f422857f12f49fcaada3fd25457dc29.png
  • $$0$$
  • $$mv$$
  • $$4 mv$$
  • $$\displaystyle \frac {2mv}{\sqrt {3}}$$
Three identical uniform rods, each of length l, 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.
  • $$\displaystyle \frac{l}{\sqrt{3}}$$
  • $$\displaystyle \frac{l}{\sqrt{2}}$$
  • $$\displaystyle \frac{l}{\sqrt{5}}$$
  • $$\displaystyle \frac{l}{\sqrt{7}}$$
In case of torque of a couple, if the axis is changed by displacing it parallel to itself, torque will
  • Increase
  • Decrease
  • Remain constant
  • None of these
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