VBQs System of Particles and Rotational Motion Class 11 Physics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 11 Physics with solutions. The following System of Particles and Rotational Motion Class 11 Physics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 11 examinations.

**System of Particles and Rotational Motion VBQs Class 11 Physics**

**Question. Three identical rods each of mass m and length l are forming an equilateral triangle. The moment of inertia of rod about an axis through its one vertex and perpendicular to the plane is **

(a) ml^{2} /3

(b) ml2 /1^{2}

(c) 3/2 ml^{2}

(d) ml^{2} /4

**Answer**

C

**Question. A disc is rolling without slipping on horizontal surface as shown in figure. Point C is the centre of disc. Point A and B are equidistant from centre of disc.**

Let VA, VC and VB are linear velocities of points A, B and C respectively. Then the relation between VA, VB and VC is

(a) V_{A} > V_{B} > V_{C}

(b) V_{B} > V_{C} > V_{B}

(c) V_{B} > V_{C} > V_{A}

(d) V_{A }< VB < V_{C}

**Answer**

B

**Question. Power of the body in rotational motion (symbols have their usual meaning)**

(a) τ.ω r r

(b) τ2ω

(c) τ.a

(d) τ.a2

**Answer**

A

**Question. A disc of radius R is moving with velocity of centre of mass v and angular speed ω as shown in the figure. The angular momentum of disc about point O is **

(a) Iω

(b) Rmv

(c) Iω + Rmv

(d) Iω – Rmv

**Answer**

D

**Question. A ball of mass 1 kg moving with a velocity of 100 ms–1, strikes a wall at an angle 60º (as shown in figure). If the ball rebounds with same speed, the impulse acted on it is **

(a) 100 N-s

(b) 100√3 N-s

(c) 200 N-s

(d) 200 3 N-s

**Answer**

B

**Question. Moment of inertia of rod about an axis AA′ passing through point P according to diagram (mass of rod = M, length of rod = L) is**

(a) ML^{2} /12

(b) ML^{2} /3

(c) 7ML^{2} /48

(d) 5ML^{2} /48

**Answer**

C

**Question. The disc in the figure is in pure rolling, with respect to the plank which is moving with V. The velocity of point P on the disc with respect to ground is **

(a) Zero

(b) V

(c) 2V

(d) v/2

**Answer**

B

**Question. The position of centre of mass of a system consisting of two particles of masses m _{1} and m_{2} seperated by distance L apart, from m_{1} will**

(a) m1L /m1+m2

**(b) m2L /**m1

**+m2**

(c) m2/m1

(d) L/2

**Answer**

B

**Question. Which of the following statement is incorrect? (symbols have usual meanings)**

(a) K.E. of a point mass body in motion is always 1/2 mv^{2}

(b) K.E. of a rigid body in translatory motion is 1/2 mv^{2}_{cm}

(c) K.E. of a rigid body in pure rotatory motion is 1/2 lω^{2}

(d) K.E. of a point mass revolving about an axis is 1/2 lω^{2} which is different from 1/2 mv^{2}

**Answer**

D

**Question. A rod of one metre is initially at rest and makes an angle 30° with vertical as shown in figure. The angular acceleration of rod, just after it is released, is**

(a) g/4

(b) 3g/2

(c) 3g/4

(d) g /2

**Answer**

C

**Question. Let I _{1} and I_{2} be the moment of inertia of a uniform square plate about axes shown in the figure. Then the rate I_{1} : I_{2} is **

**Answer**

D

**Question. The moment of inertia in terms of angular momentum (L) and kinetic energy (K) is**

(a) L2/K

(b) L2/2K

(c) 1/2K^{2}

(d) 1/2K

**Answer**

B

**Question. A person of mass m stands at the centre of a tablemoment of intertia I and rotating with angular velocity ω. If the person moves distance ‘a’ from the centre along the diameter, what will be the new angular velocity of rotating table?**

(a) Iω/ma2

(b) Remain same

(c) Iω/2ma2

(d) Iω/1+ma2

**Answer**

D

**Question. A particle of mass 500 gm, having position vector r = (2iˆ + 6 jˆ) metre starts moving with speed 3 m/s parallel to positive x-axis. Its angular momentum about origin is**

(a) 9kˆ J-s

(b) − 9kˆ J-s

(c) 3kˆ J-s

(d) − 3kˆ J-s

**Answer**

B

**Question. A solid cylinder of mass M and radius R rolls down an inclined plane of height h. The angular velocity of the cylinder when it reaches the bottom of the plane will be **

**Answer**

C

**Question. A disc, sphere, ring and hollow spherical shell all are rolling without slipping on a horizontal planes. The ratio of linear translational kinetic energy to rolling kinetic energy is minimum for**

(a) Disc

(b) Sphere

(c) Ring

(d) Hollow spherical shell

**Answer**

C

**Question. Moment of inertia of a thin rod of length L mass M about its perpendicular bisector axis is I. If the rod is bend through 60º about midpoint on a plane perpendicular to the axis, then new moment of inertia of the rod will be**

(a) I

(b) I/2

(c) 3 I

(d) 3I/2

**Answer**

A

**Question. A solid sphere is rolling without slipping on a rough horizontal surface. The horizontal surface ends up as a rough inclined plane as shown. As the sphere rolls up on the plane, the force of friction on the sphere is **

(a) Along the plane upward

(b) Along the plane downward

(c) Zero

(d) Along horizontal, backward

**Answer**

A

**Question. Three particles A, B and C each of mass 2 kg are kept in xy plane as shown in figure. The coordinates of their centre of mass are **

(a) (1, 1)

(b) (1, 2)

(c) (1/2, 1)

(d) (1/2, 3/2)

**Answer**

B

**Question. A uniform rod of length 2L has a constant mass per unit length (μ). The moment of inertia of the rod about an axis which is a perpendicular be-sector of the rod is**

(a) 2/3 μL^{2}

(b) 2/3 μL^{3}

(c) 8/3 μL^{3}

(d) 4/3 μL^{2}

**Answer**

B

**Question. A uniform thin rigid rod is free to rotate about the horizontal axis passing perpendicularly to its length through its one end. When released from rest from position OA, then during the journey from OA to OB position [ω → angular speed]**

(a) ω increases

(b) ω decreases

(c) ω remains constant

(d) ω may increase or decrease

**Answer**

A

**Question. From a uniform square lamina a quarter lamina is cut off as shown in figure. Then the position of centre of mass of remaining portion with respect to original centre of mass lies in the region**

(a) A

(b) C

(c) B

(d) D

**Answer**

C

**Question. Six identical rods each of mass m and length l are arranged to form a regular hexagon. Then the moment of inertia of arrangement about axis passing through centre and perpendicular to the plane**

(a) 5ml2

(b) 9/2 ml2

(c) 2ml2

(d) ml2 /2

**Answer**

A

**Question. Two perfectly smooth (no friction) disc of moment of inertia I1 and I2 are rotating about their axis with angular velocity ω1 and ω2 in same sence. If they are placed in contact with each other so that their axes are common, then their new angular velocity will be**

(a) l1ω_{1} + l_{2}ω_{2} / l_{1} + l_{2}

(b) They will exchange their angular velocity

(c) There will be no change in their respective angular velocities as these are perfectly smooth

(d) They can’t be placed in contact as they will push each other

**Answer**

C

**Question. Two discs made up of same sheet which is of uniform thickness. Masses of discs are in the ratio of 1 : 4. If particle on outer peripheri of both disc have same linear velocity when discs are in pure rotational motion about their axis then the ratio of their angular momentum will be**

(a) 1 : 2

(b) 1 : 4

(c) 1 : 8

(d) 1 : 16

**Answer**

C

**Question. A uniform disc of mass M is rotating about its axis with angular velocity ω. Now four identical masses each M/4 are placed gently at the ends of two mutually perpendicular diameters of disc. The new angular velocity will be**

(a) ω

(b) ω/2

(c) ω/3

(d) 2ω

**Answer**

C

**Question. The diagram shows the top view of a cricket ball moving in the right side along x-axis and spinning clockwise. The ball will**

(a) Swing toward +ve y-axis

(b) Swing toward –ve y-axis

(c) Continue to move along x-axis

(d) Any of the above depending on the ratio v/ω

**Answer**

B

**Question. A disc is rolling on a horizontal surface with its linear speed v. Velocity of point P at the instant shown in figure is **

(a) 2v cos (θ/2)

(b) 2v sin (θ/2)

(c) vcos (θ/2)

(d) vsin (θ/2)

**Answer**

B

**Question. A solid cylinder in rolling down on a rough inclined plane. Angle of inclination of plane is 30°. The acceleration of solid cylinder is**

(a) g

(b) gsin30°

(c) g/3

(d) g + gsin30°

**Answer**

C

**Question. The instantaneous angular acceleration is defined as **

**Answer**

B

**Question. A solid disc is rolling without slipping on a frictionless surface shown in figure with translational velocity v m/s. If it is just to climb the inclined frictionless surface, then v should be **

(a) √2gh

(b) √4/3 gh

(c) √gh

(d) √1/3 gh

**Answer**

A

**Question. In case of pure rolling of a disc on a rough ground. **

The ratio of speed at topmost point and at the centre of mass is

(a) 2 : 1

(b) 1 : 2

(c) 1 : 1

(d) 2 :1

**Answer**

A

**Question. The angular momentum of particle about origin moving with uniform velocity moving along straight line as shown in the figure is**

(a) Constant

(b) First increases then decreases

(c) First decreases then increases

(d) Decreases continuously

**Answer**

A

**Question. A cubical block of mass M and edge ‘a’ slides down on an rough inclined plane of inclination θ with uniformvelocity. The torque of friction force on the block about its centre has a magnitude of**

(a) Zero

(b) mg a sinθ

(c) mg a/2 sinθ

(d) mg a/2 cosθ

**Answer**

C

**Question. A particle of mass m is projected with a velocity (aî + bĵ) from ground. The angular momentum of particle about point of projection when particle is at topmost point**

(a) ma^{2}b/2g

(b) mab^{2}/2g

(c) 2ma^{2}b/g

(d) mab^{2}/g

**Answer**

B

**Question. The velocity of centre of mass of disc rolling on an inclined plane changed from v to 2v, then increase in its kinetic energy will be (m – mass of disc)**

(a) 9/4 mv2

(b) mv2/2

(c) mv2

(d) 3mv2

**Answer**

A

**Question. There is sufficient friction between the ring and incline so that when the ring released, moves under pure rolling. The velocity of centre of ring at bottom is **

(a) √2gh

(b) √gh

(c) √1/3 gh

(d) √12/3 gh

**Answer**

B

**Question. Three particles are placed at the corners of a triangle as shown in figure. Their centre of mass is at a position **

**Answer**

C

**Question. A disc is in pure rolling on the plank which is moving with 10 m/sec as shown. The uppermost point of the disc has a speed of 30 m/sec Radius of the disc is 1 m. Its angular speed is**

(a) 30 rad/sec

(b) 10 rad/sec

(c) 20 rad/sec

(d) 40 rad/sec

**Answer**

B

**Question. A uniform thin circular ring of mass M and radius R is bend in 8 shaped planar loop. Assuming the two smaller loops to be identical, what is the moment of inertia of this system about an axis passing through their common point and perpendicular to their plane?**

(a) MR2/2

(b) 3/4 MR2

(c) 4/3 MR2

(d) 2 MR2

**Answer**

A

**Question. A wheel is in uniform pure rolling along a level road. ****The speed of translational motion of the wheel axis is v. What is the speeds of the points A, B and C on the wheel rim relative to the road at the instant shown in the figure? **

(a) vA = 0, vB = 2v, vC = v

(b) vA = 0, vB = 2v, vC = 2v

(c) vA = v, vB = v, vC = v

(d) vA = v/2, vB = 2v, vC = v

**Answer**

B

**Question. Two balls moving with same speed starts to move on a rough inclined plane. Ball A is solid and ball B is hollow. There is sufficient friction for pure rolling. If maximum height attained by balls A and B are h1 and h2 respectively, then which of the following relation is correct? **

(a) h_{1} = h_{2}

(b) h_{1} > h_{2}

(c) h_{2} > h_{1}

(d) h_{2} >> h_{1}

**Answer**

C

**Question. A coin of radius r rolls without slipping on smooth horizontal floor. If velocity of centre of mass is 10 m/s, then linear velocity of point P is **

(a) 15 ms^{–1}

(b) 5 ms^{–1}

(c) 20 ms^{–1}

(d) 10 ms^{–1}

**Answer**

A

**Question. The position vector of two particles of mass m _{1}=1kg, **

**Answer**

A

**Question. The figure is a part of disc. Mass of this part is M and radius is R. The moment of intertia about the given axis is**

(a) MR^{2}/6

(b) MR^{2}/2

(c) MR^{2}/3

(d) 3MR^{2}/4

**Answer**

B

**Question. The moment of inertia of a uniform rod of mass m and length 2l with two particles of mass m each at its ends. Find the MOI of the system about the shown axis**

(a) 1/3 ml^{2}

(b) 2/3 ml^{2}

(c) 5/3 ml^{2}

(d) 7/3 ml^{2}

**Answer**

D

**Question. The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height h from rest without sliding is**

**Answer**

D

**Question. Three thin rods each of length L and mass M are placed along x, y and z-axes in such a way that one end of each of the rods is at the origin. The moment of inertia of this system about z-axis is **

(a) 2ML^{2} /3

(b) 4ML^{2}/3

(c) 5ML^{2}/3

(d) ML^{2}/3

**Answer**

A

**Question. Four identical thin rods each having mass m and length l are arranged in the form of square. Find out the moment of inertia of the system about an axis AD. **

(a) 2ml^{2} /3

(b) ml^{2} /3

(c) 5ml^{2} /3

(d) 7ml^{2} /5

**Answer**

C

**Question. A hole of radius a is cut in a uniform circular plate of radius R as shown. Find out the distance of the centre of mass of the residual plate from the centre of the original plate is **

(a) ab/R

(b) a^{2}b/b^{2}–a^{2}

(c) a^{2}b/R^{2}–b^{2}

(d) a^{2}b/R^{2}–a^{2}

**Answer**

D

**Question. A uniform circular ring is rolling on a horizontal surface without slipping. If its total kinetic energy is E, then its rotational and translational kinetic energies are respectively**

(a) E/2 , E/2

(b) 2E/3 , E/3

(c) 3E/4 , E/4

(d) E/3 , 2E/3

**Answer**

A

**Question. In the shown figure, the disc is in pure rolling motion with velocity of centre of mass is v. **

**The angular momentum of the disc about origin **

(a) mvR/2

(b) mvR

(c) 3/2 mvR

(d) 2 mvR

**Answer**

C

**Question. A uniform rod of length L and mass M is resting on a vertical wall and horizontal surface The vertical wall is smooth and co-efficient of friction between the rod and horizontal surface is μ For equilibrium of rod, what is the minimum value of θ **

(a) tan^{–1} (1/μ)

(b) tan^{–1} (2/μ)

(c) tan^{–1} (1/2μ)

(d) tan^{–1} (μ/2)

**Answer**

C

**Question. A uniform rod of length L is kept horizontal by two vertical strings as shown. If tensions in the left and right strings are T _{1} and T_{2} respectively then T_{1}/T_{2} is equal to **

(a) 1/3

(b) 1/6

(c) 3

(d) 6

**Answer**

A

**Question. A disc is rolling (without slipping) on a frictionless surface about its centre C and Q and P are two points equidistant from C. Let VP, VQ and VC be the magnitudes of velocities of points P, Q and C respectively, then **

(a) V_{Q }> V_{C }> V_{P}

(b) V_{Q} < V_{C} < V_{P}

(c) V_{Q} = V_{P} , V_{C} = 1/2 V_{P}

(d) V_{Q} < V_{C} > V_{P}

**Answer**

A

**Question. A rigid body rotates about a fixed axis with variable angular velocity given as(α-βt) at time t, where α and β are constants. The angle through which it rotates before it comes to rest is**

(a) α2/2β

(b) α2–β2/2α

(c) α2–β2/2β

(d) α(α–β)/2

**Answer**

A

**Question. In the figure, m _{1} > m_{2}. The connecting string is ideal and does not slip over pulley. Moment of inertia of pulley is I. Acceleration of the blocks has magnitude **

**Answer**

B

**Question. A string is wrapped over the edge of a uniform disc and free end is fixed with the ceiling. The disc moves down, unwinding the string. Then find out the downward acceleration of the disc. **

(a) g

(b) g/3

(c) g/2

(d) 2g/3

**Answer**

D