InterviewSolution
Saved Bookmarks
InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
A wheel is free to rotate about its own axis without friction. A rope is wound around the wheel. If other end of rope is pulled with a constant force, then true statement from the following isA. constant torque is produced and the wheel is rotated with constant angular velocityB. constant torque is produced and the wheel is rotated with constant angular accelerationC. variable torque is produced and the wheel is rotated with variable angular velocityD. variable torque is produced and the wheel is rotated with variable angular acceleration |
| Answer» Correct Answer - B | |
| 52. |
A rigid body is in pure rotation, that is, undergoing fixed axis rotation. Then which of the following statement(s) are true?A. You can find two points in the body in a plane perpendicular to the axis of rotation having same velocityB. you can find two points in the body in a plane perpendicular to the axis of rotation having same accelerationC. speed of fall the particles lying on the curved surface of a cylinder whose axis coincides with the axis of rotation is sameD. angular speed of the body is same as seen from any points in the body |
|
Answer» Correct Answer - C::D All points in the body, in plane perpendicular to the axis of rotation, revolve in concentric circles. All points lying on the circle of same radius have same speed (and also same magnitude of acceleration) but different directions of velocity (also different directions of acceleration) hence there cannot be two points in the given plane with same velocity or with same acceleration. As mentioned above, points lying on circle of same radius have same speed. Angular speed of body at any instant wrt any point on the body is same by definition. |
|
| 53. |
A unifrom square plate has a small piece `Q` of an irregular shape removed and glued to the centre of the plate leaving a hole behind [Fig.] The moment of inertia about the z-axis is than A. increasedB. decresedC. the sameD. changed in unpredicted manner. |
|
Answer» Correct Answer - B In the given diagram, when the small pice `Q` removed and glued to the centre of the centre of the plate the mass comes closet to the z-axis hence moment of inertia decreases. |
|
| 54. |
Two rings of same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass the ring `= m`, radius `= r`)A. `(MR^(2))/2`B. `MR^(2)`C. `(3MR^(2))/4`D. `2MR^(2)` |
|
Answer» Correct Answer - C `I=I_(1)+I_(2)` where `I_(1)=MR^(2)` and `I_(2)=(MR^(2))/2` |
|
| 55. |
If the resultant of all the external forces acting on a system of particles is zero. Then from an inertial frame, one can surely say thatA. linear momentum of the system does not change in timeB. kinetic energy of the system changes in timeC. angular momentum of the system does not change in timeD. potential energy of the system does not change in time |
|
Answer» Correct Answer - A::B As external force is zero. `P` is constant but `K.E.` increases. Due to external torque, angular momentum changes. `P.E.` also changes. |
|
| 56. |
Then moment of inertia of a rigid body depends on (A) mass of body (B) position of axis of rotation (C) time period of its rotation (D) angular velocity of the bodyA. `A` and `B` are trueB. `B` and `C` are trueC. `C` and `D` are trueD. `A` and `D` are true |
| Answer» Correct Answer - A | |
| 57. |
Two bodies with moment of inertia `I_1` and `I_2 (I_2 gt I_1)` are rotating with same angular momentum. If `K_1` and `K_2` are their K.E.s, thenA. `K_(2)gtK_(1)`B. `K_(2)ltK_(1)`C. `K_(1)=K_(2)`D. `K_(2)geK_(1)` |
| Answer» Correct Answer - B | |
| 58. |
A particle of mass `1 kg` is projected with an initial velocity `10 ms^(-1)` at an angle of projection `45^(@)` with the horizontal. The average torque acting on the projectile and the time at which it strikes the ground about the point of projection in newton meter isA. `25`B. `50`C. `75`D. `100` |
|
Answer» Correct Answer - B `tau=(dL)/(dt)=m(u^(2)cos^(2)theta)` |
|
| 59. |
A particle performing uniform circular motion gas angular momentum `L`. If its angular frequency is double and its kinetic energy halved, then the new angular momentum is :A. `4L`B. `2L`C. `L/2`D. `L/4` |
| Answer» Correct Answer - D | |
| 60. |
A particle of mass `5g` is moving with a uniform speed of `3sqrt2 cm//s` in the `x-y` plane along the line `y=x+4`. The magnitude of its angular momentum about the origin in `g cm^(2)//s` isA. zeroB. `60`C. `30`D. `30/(sqrt(2))` |
|
Answer» Correct Answer - B From the diagram, `OC=OA sin45^(@)=4xx1/(sqrt(2))=2sqrt(2)cm` Angular momentum `=mv(OC)=5(3sqrt(2))(2sqrt(2))= 60 gm cm^(2)s^(-1)` |
|
| 61. |
Two bodies with masses `m_1` and `m_2(m_1gtm_2)` are joined by a string passing over fixed pulley. Assume masses of the pulley and thread negligible. Then the acceleration of the centre of mass of the system `(m_1+m_2)` isA. `(g(m_(1)-m_(2)))/((m_(1)+m_(2)))`B. `(g(m_(1)-m_(2))^(2))/((m_(1)+m_(2)))`C. `(g(m_(1)+m_(2)))/((m_(1)-m_(2)))`D. `(g(m_(1)+m_(2)))/((m_(1)-m_(2)))` |
|
Answer» Correct Answer - B `(a_(cm))_(y)=(F_(ext))/(M)=((m_(1)+m_(2))g-2T)/(m_(1)+m_(2))to(1)` But `T=(2m_(1)m_(2)g)/(m_(1)+m_(2))to(2)` |
|
| 62. |
A particle of mass `80` units is moving with a uniform speed `v=4 sqrt 2` units in `XY` plane, along a line `y=x+5`. The magnitude of the angular momentum of the particle about the origin isA. `1600` unitsB. `160sqrt(2)` unitsC. `152sqrt(2)` unitsD. `16sqrt(2)` units |
|
Answer» Correct Answer - A `bar(L)=bar(r)xxbar(p)=m(bar(r)xxbar(v))` |
|
| 63. |
The diameter of a disc is `1m`. It has a mass of `20kg`. It is rotating about its axis with a speed of `120` rotations in one minute. Its angular momentum in `kg m^2//s` isA. `13.4`B. `31.4`C. `41.4`D. `43.4` |
|
Answer» Correct Answer - B `L=Iomega`Where `I=(mr^(2))/2, omega=2pin` |
|
| 64. |
The mass of a uniform ladder of length `5m` is `20kg`. A person of mass `60kg` stand on the ladder at a height of `2m` from the bottom. The position of centre of mass of the ladder and man from the bottom isA. `1.256 m`B. `2.532m`C. `3.513m`D. `2.125m` |
|
Answer» Correct Answer - D Mass of ladder acts at `2.5 m` Mass of man acts at `2m` `y=(m_(1)y_(1)+m_(2)y_(2))/(m_(1)+m_(2))` |
|
| 65. |
Two blocks A and B of equal masses are attached to a string passing over a smooth pulley fixed to a wedge as shown in figure. Find the magnitude of acceleration of centre of mass of the two blocks when they are released from rest. Neglect friction. A. `((sqrt(3)-1)/(4sqrt(2))g)`B. `(sqrt(3)-1)g`C. `g/2`D. `((sqrt(3)-1)/(sqrt(2)))g` |
|
Answer» Correct Answer - A Acceleration of system, `a=(mg sin 60-mg sin 30)/(2m)` `a=((sqrt(3)-1)/4) g`, Now `bar(a)_(cm)=(mbar(a)_(1)+mbar(a)_(2))/(2m)` here `bar(a)_(1)` and `bar(a)_(2)` are `((sqrt(3)-1)/4)g` at right angles hence, `a_(cm)=(sqrt(2)a)/2=((sqrt(3)-1)/(4sqrt(2)))g` |
|
| 66. |
A block of mass `m=4kg` is attached to a spring of spring constant `(k=32 Nm^(-1))` by a rope that hangs over a pulley of mass `M=8kg` If the system starts from rest with the spring unstretched, find the speed of the block after it falls `1m`. Treat the pulley as a disc, so `I=1/2 MR^2` |
|
Answer» Since the rim of the pullely moves at the same speed as the block, the speed of the block and the angular velocity of the pulley related by `v= omegaR` when the block falls by a distance `x`, its potential energy decrease `(DeltaU_(g)=-mgx)`, the potential energy of the spring increases `(Delta_(s)=+1/2kx^(2)`), and both the block and the pulley gain `KE` `(DeltaK=1/2mv^(2)+1/2Iomega^(2))` From the conservation of mechanical energy, `DeltaK+DeltaU=0`, `1/2mv^(2)+1/2I(v/R)^(2)+1/2kx^(2)-mgx=0` `1/2(m+M/2)v^(2)+1/2kx^(2)-mgx=0` Putting `m=4kg, M=8 kg, k=32 Nm^(-1), x=1 m` `1/2(4+8/2)v^(2)+1/2(32)(1)^(2)-(4)(10)(1)=0` `4v^(2)+16-40=0 rArrv=2.4 mx^(-1)` |
|
| 67. |
A rope thrown over a pulley has a ladder with a man of mass `m` on one of its ends and a counter balancing mass `M` on its other end. The man climbs with a velocity `v_r` relative to ladder. Ignoring the masses of the pulley and the rope as well as the friction on the pulley axis, the velocity of the centre of mass of this system is:A. `m/M v_(r)`B. `m/(2M)v_(r)`C. `M/m v_(r)`D. `(2M)/m v_(r)` |
|
Answer» Correct Answer - B The masses of load, ladder and man are `M,M-m` and `m` repectively. Their velocities are `v`(upward),`-v` and `v_(r)-v` respectively ` :. V_(cm)=(sum m_(i)v_(i))/(summ_(i))` `=(M(v)+(M-m)(-v)+m(v_(r)-v))/(2M)=m/(2M)v_(r)` |
|
| 68. |
A boy of mass `50kg` is standing at one end of a boat of length `9m` and mass `400kg`. He runs to the other end. The distance through which the centre of mass of the boat boy system moves isA. `0`B. `1m`C. `2m`D. `3m` |
|
Answer» Correct Answer - A Centre of mass does not change |
|
| 69. |
A `10 kg` boy standing in a `40 kg` boat floating on water is `20 m` away from the shore of the river. If the boy moves `8 m` on the boat towards the shore, then how far is he from the shore ? (Assume no friction between boat and water). |
|
Answer» Mass of the boy `(m)=10 kg` Mass of the boat `(M)=40 kg` Distance travelled by boy `(l)=8 m` Distance travelled by the boat in opposite direction `=(ml)/(M+m)=(10xx8)/(10+40)=1.6 m` Distance of the boy from the shore is `(20-8)+(1.6)=13.6 m` |
|
| 70. |
Six identical particles each of mass `m` are arranged at the corners of a regular hexagon of side length `L`. If the mass of one of the particle is doubled, the shift in the centre of mass isA. `L/8`B. `(sqrt(3)L)/8`C. `(3L)/16`D. `(3L)/4` |
|
Answer» Correct Answer - B `shift=(md)/(M+m)` |
|
| 71. |
Six identical particles each of mass `m` are arranged at the corners of a regular hexagon of side length `L`. If the mass of one of the particle is doubled, the shift in the centre of mass isA. `L`B. `6L//7`C. `L//7`D. `L/(sqrt(3))` |
|
Answer» Correct Answer - C shift `=(md)/(M+m)` |
|
| 72. |
An electric motor rotates a wheel at a constant angular velocity `10rps` while opposing torque is `10Nm`. The power of that electric motor isA. `120W`B. `628W`C. `314W`D. `3.14W` |
|
Answer» Correct Answer - B `p=tau omega` |
|
| 73. |
A constant torque of `1000 N-m` turns a wheel of moment of inertia `200 kg-m^2` about an axis through its centre. Its angular velocity after `3` seconds is.A. `15 rads^(-1)`B. `22 rads^(-1)`C. `28 rads^(-1)`D. `60 rads^(-1)` |
|
Answer» Correct Answer - A `tau=Ialpha,omega=alphat` |
|
| 74. |
Which of the following equation is wrongA. `vec(tau)=vec(r)xxvec(F)`B. `vec(a)_(r)=vec(r)xxvec(V)`C. `vec(a)_(r)=vec(alpha)xxvec(r)`D. `vec(V)=vec(r)xxvec(omega)` |
| Answer» Correct Answer - B | |
| 75. |
A constant torque acting on a uniform circular wheel changes its angular momentum from `A` to `4A` in `4sec`. The torque acted on it isA. `(3A)/4`B. `A/4`C. `(2A)/4`D. `(3A)/4` |
|
Answer» Correct Answer - A `tau=(L_(2)-L_(1))/t` |
|
| 76. |
Magnitude of torque is maximum in the following caseA. radius vector is perpendicular to force vectorB. radius vector is parallel to force vectorC. angle between radius vector and force vector is `45^(@)`D. angle between radius vector radius and force vector is `60^(@)` |
| Answer» Correct Answer - A | |
| 77. |
Which of the following is wrongA. direction of torque is parallel to axis of rotationB. Direction of moment of couple is perpendicular to the plane of rotation of bodyC. Torque vector is perpendicular to both position vector and force vectorD. The direction of force vector is always perpendicular to both the directions of position vector and torque vector |
| Answer» Correct Answer - D | |
| 78. |
A circular disc is rotated along clockwise direction in horizontal plane. The direction of torque isA. horizontally right sideB. horizontally left sideC. vertically upwardD. vertically downwards |
| Answer» Correct Answer - D | |
| 79. |
A uniform circular ring of radius `R` is first rotated about its horizontal axis with an angular velocity `omega_0` and then carefully placed on a rough horizontal surface as shown. The coefficient of friction between the surface and the rings `mu`. Time after which its angular speed is reduced to `0.5 omega_0` is A. `(omega_(0)muR)/(2g)`B. `(omega_(0)g)/(2muR)`C. `(2 omega_(0)R)/(mug)`D. `(omega_(0)R)/(2mug)` |
|
Answer» Correct Answer - D Taking the `tau` about `C.M.` `mu mG R=MR^(2)alpha,mug=RalpharArralpha=(mug)/R` `omega=omega_(0)-(mug)/Rt=(omega_(0))/2, :. T=(omega_(0)R)/(2mug)` |
|
| 80. |
A uniform metal rod is rotated in horizontal plane about a vertical axis passing through its end at uniform rate. The tension in the rod isA. same at all pointsB. different at differen points and maximum at centre of rodC. different at different points and minimum at axis of rotation.D. different at different points and maximum at axis of rotation |
| Answer» Correct Answer - D | |
| 81. |
A large rectangular box has been rotated with a constant angular velocity `omega_(1)` about its axis as shown in the figure. Another small box kept inside the bigger box is rotated in the same sense with angular velocity `omega_(2)` about its axis (which is fixed to floor of bigger box). A particle `P` has been identified, its angular velocity about `AB` would be A. `(omega_(2)(r_(2)-r_(1))+omega_(1)r_(2))/(r_(2))`B. `(omega_(2)(r_(2)-r_(1))+omega_(1)r_(1))/(r_(2))`C. `omega_(1)`D. `omega_(2)` |
|
Answer» Correct Answer - B `vec(V),CD=omega_(2)(r_(2)-r_(1)),vec(V),CD,AB=omega_(1)r_(1)` `vec(V)_(P),AB=vec(V)_(P),CD+vec(V)_(CD),AB` `=omega_(2)(r_(2)-r)+omega_(1)r_(1)` Angular velocity of `P` about `AB` `omega=(v_(PAB))/(r_(2))=omega_(2)(r_(2)-r_(1))+omega_(1)(r_(1))/(r_(2))` |
|
| 82. |
The pulley shown in figure has a radius 10 cm and moment of inertia 0.5 kg-m^2 about its axis. Assuming the inclined planes to be frictionless, calculate the acceleration of the 4.0 kg block. |
|
Answer» Correct Answer - 4 `(T_(1)-T_(1))R=Ialpha` `(T_(2)-T_(1))R=I(a/R)to(i)` `4g sin 45^(@)-T_(2)=4ato(ii)` `T_(1)=2g sin 45^(@)=2ato(iii)` Solving (i), (ii),(iii) we get `a=0.25 m//s^(2)` |
|
| 83. |
A particle of mass m is projected with speed u at an angle `theta` with the horizontal. Find the torque of the weight of the particle about the point of projection when the particle is at the highest point.A. `(mgu^(2)sin 2 theta)/2`B. `mgu^(2)sin 2 theta`C. `(mgu^(2)sin theta)/2`D. `1/2 m u^(2)sin 2 theta` |
|
Answer» Correct Answer - D `vec(tau)=[R/2hati+Hhatj]xxmghatj` |
|
| 84. |
Two objects of masses `1kg` and `2kg` separated by a distance of `1.2m` are rotating about their centre of mass. Find the moment of inertia of the systemA. `0.96 kgm^(2)`B. `0.48 kgm^(2)`C. `0.83 kgm^(2)`D. `0.72 kgm^(2)` |
|
Answer» Correct Answer - A `I=((m_(1)m_(2))/(m_(1)+m_(2)))r^(2)` |
|
| 85. |
A yo-yo is placed on a rough horizontal surface and a constant force `F`, which is less than its weight, pulls it vertically. Due to this A. frictional force acts towards left, so it will move towards leftB. frictional force acts towards right, so it will move towards rightC. it will move towards left, so frictional force acts towards leftD. it will move towards right so friction force acts towards right |
| Answer» Correct Answer - A | |
| 86. |
A uniform meter scale of mass `1kg` is placed on table such that a part of the scale is beyond the edge. If a body of mass `0.25kg` is hung at the end of the scale then the minimum length of scale that should lie on the table so that it does not tilt isA. `30 cm`B. `80 cm`C. `70 cm`D. `60 cm` |
|
Answer» Correct Answer - D `(50-x)1=x(0.25), x=40 cm` length of the table`=100-40=60cm` |
|
| 87. |
A uniform metal rod of length `L` and mass `M` is rotating about an axis passing throuth one of the ends perpendicular to the rod with angular speed `omega`. If the temperature increases by `t^@C` then the change in its angular velocity is proportional to which of the following ? (Coefficient of linear expansion of rod `=alpha`)A. `sqrt(omega)`B. `omega`C. `omega^(2)`D. `1/(omega)` |
|
Answer» Correct Answer - B `Iprop1/(omega).....1, I=(ML^(2))/3rArrI prop L^(2)....(2)` from (1) and (2) `omegaprop1/(L^(2))` |
|
| 88. |
A uniform cylindrical rod of mass `m` and length `L` is rotating with an angular velocity `omega`. The axis of rotation is perpendicular to its axis of symmetry and passes through one of its edge faces. If the room temperature increases by `t` and the coefficient of linear expansion is `alpha`, the change in its angular velocity isA. `2 alphaomegat`B. `alphaomegat`C. `3/2alpha omegat`D. `(alphaomegat)/2` |
|
Answer» Correct Answer - A `Iprop1/omegaimplies(Deltaomega)/(omega)=-(DeltaI)/I=2alphaDeltat` |
|
| 89. |
The radius of gyration of rod of length `L` and mass `M` about an axis perpendicular to its length and passing through a point at a distance `L//3` from one of its ends isA. `(sqrt(7))/6 L`B. `(L^(2))/9`C. `L/3`D. `(sqrt(5))/2 L` |
|
Answer» Correct Answer - C According to parallel axes theoram `I=(ML^(2))/12+M(L/6)^(2)=(4ML^(2))/36=(ML^(2))/6 :. K=L/3` |
|
| 90. |
The radius of gyration of a body about an axis at a distance of `12cm` from its centre of mass is `13cm`. Find its radius of gyration about a parallel axis through its centre of mass. |
|
Answer» By parallel axes theoram `M(13)^(2)=I_(0)+M(12)^(2)` `I_(0)=M(13^(2)-12^(2))=M(25)` Its radius of gyration about a parallel axes through its centre of mass `K=sqrt((I_(0))/M)=sqrt(25)=5 cm` |
|
| 91. |
The radius of gyration of a rotating circular ring is maximum about following axis of rotationA. natural axisB. axis passing through diameter of ringC. axis passing through tangent of ring in its planeD. axis perpendicular through tangent of ring perpendicular to plane of ring. |
| Answer» Correct Answer - D | |
| 92. |
The radius of gyration of a rotating metallic disc is independent of the following physical quantity.A. position of axis of rotationB. mass of discC. radius of discD. temperature of disc |
| Answer» Correct Answer - B | |
| 93. |
A brass disc is rotating about its axis. If temperature of disc is increased then itsA. radius of gyration increases, but moment of inertia remains the sameB. moment of inertia increases but radius of gyration remains the sameC. radius of gyration, moment of inertia both remain the sameD. radius of gyration, moment of inertia both increase |
| Answer» Correct Answer - D | |
| 94. |
The radius of gyration of body is `18cm` when it is rotating about an axis passing through centre of mass of body. If radius of gyration of same body is `30cm` about a parallel axis to first axis then, perpendicular distance between two parallel axes isA. `12 cm `B. `16 cm`C. `24 cm`D. `36 cm` |
|
Answer» Correct Answer - C `K=sqrt(k_(cm)^(2)+d^(2))` |
|
| 95. |
Identify the increasing order of radius of gyration of following bodies of same radius (I) About natural axis of circular ring (II) about diameter of circular ring (III) About diameter of circular plate (IV) about diameter of solid sphereA. `II,III,IV,I`B. `III,II,IV,I`C. `III,IV,II,I`D. `II,IV,III,I` |
| Answer» Correct Answer - C | |
| 96. |
Identify the decreasing order of radius of gyration of following bodies of same radius (I) About diameter of circular ring (II) About diameter of circular plate (III) About tangent of circular ring `bot^(r)` to its plane (IV) About tangent of circular plate in its planeA. `III,IV,II,I`B. `IV,III,I,II`C. `IV,III,II,I`D. `III,IV,I,II` |
| Answer» Correct Answer - D | |
| 97. |
Identify the correct order in which the ratio of radius of gyration to radius increases for the following bodies. (I) rolling solid sphere (II) rolling solid cylinder (III) rolling hollow sphere (IV) rolling hollow sphereA. `I,II,III,IV`B. `I,III,II,IV`C. `II,I,IV,III`D. `II,I,III,IV` |
| Answer» Correct Answer - A | |
| 98. |
When the following bodies of same radius starts rolling down on same inclined plane, identify the decreasing order of their times of descent (I) Solid cylinder , (II) hollow cylinder (III) hollow sphere ,(IV) solid sphereA. `IV,I,III,II`B. `II,III,I,IV`C. `I,IV,III,II`D. `II,III,IV,I` |
| Answer» Correct Answer - B | |
| 99. |
The increasing order of fraction of total kinetic energy associated with translatory motion of the following rolling bodies is (I) circular ring ,(II) circular plate (III) solid sphere ,(IV) hollow sphereA. `I,II,IV,III`B. `IV,I,II,III`C. `I,IV,II,III`D. `IV,I,III,II` |
| Answer» Correct Answer - C | |
| 100. |
A shaft is turning at `65rad//s` at time zero. Thereafter, angular acceleration is given by `alpha=-10rad//s^(2)-5trad//s^(2)` Where `t` is the elapsed time (a). Find its angular speed at `t=3.0` s (b). How much angle does it turn in these `3s`?A. `25 rad//sec`B. `12.5 rad//sec`C. `17 rad//sec`D. `22 rad//sec` |
|
Answer» Correct Answer - B `omega=intalphadt` |
|