# Solved papers for NEET Physics Rotational Motion NEET PYQ-Rotational Motion

### done NEET PYQ-Rotational Motion Total Questions - 64

• question_answer1) A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass m are attached gently to the opposite ends of diameter of the ring. The ring will now rotate with an angular velocity:                                  [AIPMT 1998]

A)
$\frac{\omega \,(M-2\,m)}{(M+2m)}$

B)
$\frac{\omega M}{(M+2m)}$

C)
$\frac{\omega \,M}{(M+m)}$

D)
$\frac{\omega \,(M+2\,m)}{M}$

• question_answer2) The moment of inertia of a disc of mass M and radius R about a tangent to its rim in its plane is: [AIPMT 1999]

A)
$\frac{2}{3}M{{R}^{2}}$

B)
$\frac{3}{2}M{{R}^{2}}$

C)
$\frac{4}{5}M{{R}^{2}}$

D)
$\frac{5}{4}M{{R}^{2}}$

• question_answer3) Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed with centres of three balls joined. The centre of mass of the system is located at:  [AIPMT 1999]

A)
horizontal surface

B)
centre of one of the balls

C)
line joining the centres of any two balls

D)
point of intersection of the medians

• question_answer4) A solid sphere and a hollow sphere are thrown horizontally from a cliff with equal velocities, respectively. Then which sphere reaches first on earth?                                        [AIPMT 2000]

A)
Solid sphere

B)
Hollow sphere

C)
Both sphere simultaneously

D)
We cannot say because masses of spheres are not given

• question_answer5)  ABC is a right angled triangular plate of uniform thickness. The sides are such that $AB>BC$ as shown in figure. ${{I}_{1}},\,{{I}_{2}},\,{{I}_{3}}$ are moments of inertia about AB, BC and AC respectively. Then which of the following relations is correct? [AIPMT 2000]

A)
${{I}_{1}}={{I}_{2}}={{I}_{3}}$

B)
${{I}_{2}}>{{I}_{1}}>{{I}_{3}}$

C)
${{I}_{3}}<{{I}_{2}}<{{I}_{1}}$

D)
${{I}_{3}}>{{I}_{1}}>{{I}_{2}}$

• question_answer6)  A wheel of bicycle is rolling without slipping on a level road. The velocity of the centre of mass is ${{v}_{cm}};$ then true statement is:        [AIPMT 2001]

A)
the velocity of point A is $2\,{{v}_{cm}}$ and velocity of point B is zero

B)
the velocity of point A is zero and velocity of points is $2\,{{v}_{cm}}$

C)
the velocity of point A is $2\,{{v}_{cm}}$ velocity of point B is $-\,\,{{v}_{cm}}$

D)
the velocities of both A and B w are ${{v}_{cm}}$

• question_answer7) A disc is rotating with angular velocity $\omega$. If a child sits on it, what is conserved?[AIPMT 2002]

A)
Linear momentum

B)
Angular momentum

C)
Kinetic energy

D)
Moment of inertia

• question_answer8) A circular disc is to be made using iron and aluminium. To keep its moment of inertia maximum about a geometrical axis, it should be so prepared that:                     [AIPMT 2002]

A)
aluminium at interior and iron surrounds it

B)
iron at interior and aluminium surrounds it

C)
aluminium and iron layers in alternate order

D)
sheet of iron is used at both external surfaces and aluminium sheet as inner material

• question_answer9) A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the centre of mass: [AIPMT 2002]

A)
$h=R$

B)
$h=2\text{ }R$

C)
$h=0$

D)
the acceleration will be same whatever h may be

• question_answer10) P is the point of contact of a wheel and the ground. The radius of wheel is 1 m. The wheel rolls on the ground without slipping. The displacement of point P when wheel completes half rotation is:                         [AIPMT 2002]

A)
2 m

B)
$\sqrt{{{\pi }^{2}}+4}\,m$

C)
$\pi \,m$

D)
$\sqrt{{{\pi }^{2}}+2}\,m$

• question_answer11) A rod is of length 3 m and its mass acting per unit length is directly proportional to distance x from its one end. The centre of gravity of the rod from that end will be at:             [AIPMT 2002]

A)
1.5 m

B)
2.0 m

C)
2.5 m

D)
3.0 m

• question_answer12) A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be:                         [AIPMT 2003]

A)
$\frac{(M+4m)\,\omega }{M}$

B)
$\frac{(M-4m)\,\omega }{M+4m}$

C)
$\frac{M\,\omega }{4m}$

D)
$\frac{M\,\omega }{M+4m}$

• question_answer13) A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be:                   [AIPMT 2003]

A)
$\frac{{{K}^{2}}}{{{K}^{2}}+{{R}^{2}}}$

B)
$\frac{{{R}^{2}}}{{{K}^{2}}+{{R}^{2}}}$

C)
$\frac{{{K}^{2}}+{{R}^{2}}}{{{R}^{2}}}$

D)
$\frac{{{K}^{2}}}{{{R}^{2}}}$

• question_answer14) A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom? [AIPMT 2003]

A)
$\sqrt{\frac{4}{3}gh}$

B)
$\sqrt{4gh}$

C)
$\sqrt{2gh}$

D)
$\sqrt{\frac{3}{4}gh}$

• question_answer15) The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is: [AIPMT (S) 2004]

A)
2 : 3

B)
2 : 1

C)
$\sqrt{5}:\sqrt{6}$

D)
$1\,:\,\sqrt{2}$

• question_answer16) A round disc of moment of inertia ${{I}_{2}}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia ${{I}_{1}}$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is: [AIPMT (S) 2004]

A)
$\frac{{{I}_{2}}\omega }{{{I}_{1}}+{{I}_{2}}}$

B)
$\omega$

C)
$\frac{{{I}_{1}}\omega }{{{I}_{1}}+{{I}_{2}}}$

D)
$\frac{({{I}_{1}}+{{I}_{2}})\,\omega }{{{I}_{1}}}$

• question_answer17) A wheel having moment of inertia $2\text{ }kg-{{m}^{2}}$ about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be: [AIPMT (S) 2004]

A)
$\frac{2\pi }{15}N-m$

B)
$\frac{\pi }{12}N-m$

C)
$\frac{\pi }{15}N-m$

D)
$\frac{\pi }{18}N-m$

• question_answer18) Consider a system of two particles having masses ${{m}_{1}}$ and ${{m}_{2}}$. If the particle of mass ${{m}_{1}}$ is pushed towards the mass centre of particles through a distance d, by what distance would the particle of mass ${{m}_{2}}$ move so as to keep the mass centre of particles at the original position? [AIPMT (S) 2004]

A)
$\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}d$

B)
$\frac{{{m}_{1}}}{{{m}_{2}}}d$

C)
$d$

D)
$\frac{{{m}_{2}}}{{{m}_{1}}}d$

• question_answer19)  Three particles, each of mass m grams situated at the vertices of an equilateral triangle ABC of side 1 cm (as shown in the figure). The moment [AIPMT (S) 2004] of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram$-c{{m}^{2}}$ units will be:

A)
$(3/4)\,m{{l}^{2}}$

B)
$2\,m{{l}^{2}}$

C)
$(5/4)\,\,m{{l}^{2}}$

D)
$(3/2)\,\,m{{l}^{2}}$

• question_answer20) A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $\theta$. The frictional force:        [AIPMT (S) 2005]

A)
converts translational energy to rotational energy

B)
dissipates energy as heat

C)
decreases the rotational motion

D)
decreases the rotational and translational motion

• question_answer21) Two bodies have their moments of inertia $l$ and $2l$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:            [AIPMT (S) 2005]

A)
1 : 2

B)
$\sqrt{2}\,:1$

C)
2 : 1

D)
$1:\sqrt{2}$

• question_answer22) The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is:                                    [AIPMT (S) 2005]

A)
$\frac{1}{2}\,M{{R}^{2}}$

B)
$M{{R}^{2}}$

C)
$\frac{7}{2}M{{R}^{2}}$

D)
$\frac{3}{2}M{{R}^{2}}$

• question_answer23) The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc is: [AIPMT (S) 2006]

A)
$M{{R}^{2}}$

B)
$\frac{2}{5}M{{R}^{2}}$

C)
$\frac{3}{2}M{{R}^{2}}$

D)
$\frac{1}{2}M{{R}^{2}}$

• question_answer24)  A uniform rod of length $l$ and mass m is free to rotate in a vertical plane about A. The rod initially in horizontal position is released. The initial angular acceleration of the rod is:          [AIPMT (S) 2006] (Moment of inertia of rod about A is $\frac{m{{l}^{2}}}{3}$)

A)
$\frac{3g}{2l}$

B)
$\frac{2l}{3g}$

C)
$\frac{3g}{2{{l}^{2}}}$

D)
$mg\frac{l}{2}$

• question_answer25)  A uniform rod AB of length $l$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is $\frac{m{{l}^{2}}}{3},$ the initial angular acceleration of the rod will be: [AIPMT (S) 2007]

A)
$\frac{2g}{3l}$

B)
$mg\frac{l}{2}$

C)
$\frac{3}{2}gl$

D)
$\frac{3g}{2l}$

• question_answer26) A particle of mass m moves in the XY plane with a velocity v along the straight line AB. if the angular momentum of the particle with respect to origin O is ${{L}_{A}}$ when it is at A and ${{L}_{B}}$ when it is at B, then:                     [AIPMT (S) 2007]

A)
${{L}_{A}}>{{L}_{B}}$

B)
${{L}_{A}}={{L}_{B}}$

C)
the relationship between ${{L}_{A}}$ and ${{L}_{B}}$ depends upon the slope of the line AB

D)
${{L}_{A}}<{{L}_{B}}$

• question_answer27) The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is                                          [AIPMPT (S) 2008]

A)
$\sqrt{3}:\sqrt{2}$

B)
$1:\sqrt{2}$

C)
$\sqrt{2}:1$

D)
$\sqrt{2}:\sqrt{3}$

• question_answer28) A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is ${{90}^{o}}$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is [AIPMPT (S) 2008]

A)
$\frac{M{{L}^{2}}}{24}$

B)
$\frac{M{{L}^{2}}}{12}$

C)
$\frac{M{{L}^{2}}}{6}$

D)
$\frac{\sqrt{2}M{{L}^{2}}}{24}$

• question_answer29)  A circular disk of moment of inertia ${{I}_{t}}$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ${{\omega }_{t}}$. Another disk of moment of inertia ${{I}_{b}}$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed ${{\omega }_{f}}$. The energy lost by the initially rotating disc due to friction is [AIPMT (S) 2010]

A)
$\frac{1}{2}\frac{I_{b}^{2}}{({{I}_{t}}+{{I}_{b}})}\omega _{i}^{2}$

B)
$\frac{1}{2}\frac{I_{t}^{2}}{({{I}_{t}}+{{I}_{b}})}\omega _{i}^{2}$

C)
$\frac{1}{2}\frac{{{I}_{b}}-{{I}_{t}}}{({{I}_{t}}+{{I}_{b}})}\omega _{i}^{2}$

D)
$\frac{1}{2}\frac{{{I}_{b}}{{I}_{t}}}{({{I}_{t}}+{{I}_{b}})}\omega _{i}^{2}$

• question_answer30) The solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on a inclined plane. Both roll down without slipping. Which one will reach the bottom first? [AIPMT (M) 2010]

A)
Both together only when angle of inclination of plane is ${{45}^{o}}$

B)
Both together

C)
Hollow cylinder

D)
Solid cylinder

• question_answer31)  (1) Centre of gravity (CG) of a body is the point at which the weight of the body acts. (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius. (3) To evaluate the gravitational field intensity due to anybody at an external point, the entire mass of the body can be considered to be concentrated at its CG. (4) The radius of gyration of anybody rotating about an axis is the length of the perpendicular dropped from the CG of the body to the axis. Which one of the following pairs of statements is correct?                                 [AIPMT (M) 2010]

A)
(4) and (1)

B)
(1) and (2)

C)
(2) and (3)

D)
(3) and (4)

• question_answer32) A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $\omega$. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by                     [AIPMT (M) 2010]

A)
$\frac{(M+2m)\omega }{2m}$

B)
$\frac{(M+2m)\omega }{2m}$

C)
$\frac{(M+2m)\omega }{M}$

D)
$\frac{M\omega }{M+2m}$

• question_answer33) The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its mid-point and perpendicular to its length is ${{I}_{0}}$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is                           [AIPMT (S) 2011]

A)
${{I}_{0}}+M{{L}^{2}}/4$

B)
${{I}_{0}}+2M{{L}^{2}}$

C)
${{I}_{0}}+M{{L}^{2}}$

D)
${{I}_{0}}+M{{L}^{2}}/2$

• question_answer34) When a mass is rotating in a plane about a fixed point, its angular momentum is directed along [AIPMT (S) 2012]

A)
a line perpendicular to the plane of rotation

B)
the line making an angle of ${{45}^{o}}$ to the plane of rotation

C)

D)
the tangent to the orbit

• question_answer35) Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by [AIPMT (S) 2012]

A)
3.0 m

B)
2.3 m

C)
zero

D)
0.75 m

• question_answer36) A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity $4\,\,m{{s}^{-1}}$. It collides with a horizontal spring of force constant $200\,N{{m}^{-1}}$. The maximum compression produced in the spring will be [AIPMT (S) 2012]

A)
0.5 m

B)
0.6 m

C)
0.7 m

D)
0.2 m

• question_answer37)  ABC is an equilateral triangle with O as its centre. ${{F}_{1}},{{F}_{2}}$ and ${{F}_{3}}$  represent three forces acting along the sides  AB, BC and AC respectively. If the total torque about O is zero then the magnitude of ${{F}_{3}}$ is  [AIPMT (S) 2012]

A)
${{F}_{1}}+{{F}_{2}}$

B)
${{F}_{1}}-{{F}_{2}}$

C)
$\frac{{{F}_{1}}+{{F}_{2}}}{2}$

D)
$2({{F}_{1}}+{{F}_{2}})$

• question_answer38)  The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through               [AIPMT (M) 2012]

A)
B

B)
C

C)
D

D)
A

• question_answer39) Three masses are placed on the x-axis: 300 g at origin, 500 g at $x=40\,cm$ and $400\,g$ at $x=70\text{ }cm$. The distance of the centre of mass from the origin is                       [AIPMT (M) 2012]

A)
40 cm

B)
45 cm

C)
50 cm

D)
30 cm

• question_answer40)  A rod PQ of mass M and length L is hinged at end P. The rod is kepts horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is [NEET 2013]

A)
$\frac{3g}{2L}$

B)
$\frac{g}{L}$

C)
$\frac{2g}{L}$

D)
$\frac{2g}{3L}$

• question_answer41) A small object of uniform density rolls up a curved surface with an initial velocity v'. It reaches up to a maximum height of $\frac{3{{\upsilon }^{2}}}{4g}$ with respect to the initial position. The object is        [NEET 2013]

A)
ring

B)
solid sphere

C)
hollow sphere

D)
disc

• question_answer42) A solid cyclinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of $2\,\,rev/{{s}^{2}}$ is [NEET 2014]

A)
25 N

B)
50 N

C)
78.5 N

D)
157 N

• question_answer43) The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is                     [NEET 2014]

A)
5 : 7

B)
2 : 3

C)
2 : 5

D)
7 : 5

• question_answer44)  A rod of weight w is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is [NEET 2015 ]

A)
$\frac{wx}{d}$

B)
$\frac{wd}{x}$

C)
$\frac{w(d-x)}{x}$

D)
$\frac{w(d-x)}{d}$

• question_answer45)  A mass m moves in a circle on a smooth horizontal plane with velocity ${{v}_{0}}$ at a radius ${{R}_{0}}$. The mass is attached to a string which passes through a smooth hole in the plane as shown. [NEET 2015 ] The tension in the string is increased gradually and finally m moves in a circle of radius $\frac{{{R}_{0}}}{2}$. The final value of the kinetic energy is

A)
$mv_{0}^{2}$

B)
$\frac{1}{4}mv_{0}^{2}$

C)
$2\,mv_{0}^{2}$

D)
$\frac{1}{2}mv_{0}^{2}$

• question_answer46)  Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX, which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX axis is [NEET 2015 ]

A)
$\frac{11}{5}m{{r}^{2}}$

B)
$3\,m{{r}^{2}}$

C)
$\frac{16}{5}m{{r}^{2}}$

D)
$4\,m{{r}^{2}}$

• question_answer47)  Point masses ${{m}_{1}}$ and ${{m}_{2}}$ are placed at the opposite ends of a rigid rod of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass, so that the work required to set the rod rotating with angular velocity ${{\omega }_{0}}$ is minimum, is given by  [NEET 2015 (Re)]

A)
$x=\frac{{{m}_{1}}L}{{{m}_{1}}+{{m}_{2}}}$

B)
$x=\frac{{{m}_{1}}}{{{m}_{2}}}L$

C)
$x=\frac{{{m}_{2}}}{{{m}_{1}}}L$

D)
$x=\frac{{{m}_{2}}L}{{{m}_{1}}+{{m}_{2}}}$

• question_answer48) A force $\mathbf{F}=\alpha \,\mathbf{\hat{i}}+3\,\mathbf{\hat{j}}+6\,\mathbf{\hat{k}}$ is acting at a point$\mathbf{r}=2\,\mathbf{\hat{i}}-6\,\mathbf{\hat{j}}-12\,\mathbf{\hat{k}}$. The value of a for which angular momentum about origin is conserved is [NEET 2015 (Re)]

A)
- 1

B)
2

C)
zero

D)
1

• question_answer49) An automobile moves on a road with a speed of $54\,\,km\,\,{{h}^{-1}}$. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is $3\,\,kg\,\,{{m}^{2}}$. If the vehicle is brought to rest in 15s, the magnitude of average torque transmitted by its brakes to the wheel is    [NEET 2015 (Re)]

A)
$6.66\,\,kg\,\,{{m}^{2}}{{s}^{-2}}$

B)
$8.58\,\,kg\,\,{{m}^{2}}{{s}^{-2}}$

C)
$10.86\,\,kg\,\,{{m}^{2}}{{s}^{-2}}$

D)
$2.86\,\,kg\,\,{{m}^{2}}{{s}^{-2}}$

• question_answer50) From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre? [NEET - 2016]

A)
$15\,M{{R}^{2}}/32$

B)
$13\,M{{R}^{2}}/32$

C)
$11\,M{{R}^{2}}/32$

D)
$9\,M{{R}^{2}}/32$

• question_answer51) The intensity at the maximum in a Young's double slit experiment is ${{I}_{0}}$. Distance between two slits is $d=5\lambda ,$ where $\lambda$ the wavelength of light is used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance $D=10\,d$?   [NEET - 2016]

A)
${{I}_{0}}$

B)
$\frac{{{I}_{0}}}{4}$

C)
$\frac{3}{4}{{I}_{0}}$

D)
v

• question_answer52) A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first? [NEET - 2016]

A)
Disk

B)
Sphere

C)
Both reach at the same time

D)
Depends on their masses

• question_answer53) Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ${{\omega }_{1}}$ and ${{\omega }_{2}}$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is                              [NEET-2017]

A)
$\frac{l}{8}{{({{\omega }_{1}}-{{\omega }_{2}})}^{2}}$

B)
$\frac{1}{2}l{{({{\omega }_{1}}+{{\omega }_{2}})}^{2}}$

C)
$\frac{1}{4}l{{({{\omega }_{1}}-{{\omega }_{2}})}^{2}}$

D)
$l{{({{\omega }_{1}}-{{\omega }_{2}})}^{2}}$

• question_answer54) A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?                        [NEET-2017]

A)
$~5\text{ }m/{{s}^{2}}$

B)
$~25\text{ }m/{{s}^{2}}$

C)
$~0.25\text{ }rad/{{s}^{2}}$

D)
$~25\text{ }rad/{{s}^{2}}$

• question_answer55)  Which of the following statements are correct? [NEET-2017] [a] Centre of mass of a body always coincides with the centre of gravity of the body. [b] Centre of mass of a body is the point at which the total gravitational torque on the body is zero [c] A couple on a body produce both translational and rotational motion in a body. [d] Mechanical advantage greater than one means that small effort can be used to lift a large load.

A)
[c] and [d]

B)
[b] and [d]

C)
[a] and [b]

D)
[b] and [c]

• question_answer56)  A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter$\text{AB=D}$. The height h is equal to [NEET - 2018]

A)
$\frac{7}{5}D$

B)
$D$

C)
$\frac{3}{2}D$

D)
$\frac{5}{4}D$

• question_answer57) Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation                                              [NEET - 2018]

A)
${{\text{W}}_{\text{B}}}\text{}{{\text{W}}_{\text{A}}}\text{}{{\text{W}}_{\text{C}}}$

B)
${{\text{W}}_{\text{A}}}\text{}{{\text{W}}_{\text{B}}}\text{}{{\text{W}}_{\text{C}}}$

C)
${{\text{W}}_{\text{C}}}\text{}{{\text{W}}_{\text{B}}}\text{}{{\text{W}}_{\text{A}}}$

D)
${{\text{W}}_{\text{A}}}\text{}{{\text{W}}_{\text{C}}}\text{}{{\text{W}}_{\text{B}}}$

• question_answer58) The moment of the force, $\overrightarrow{\text{F}}\text{=4}\widehat{\text{i}}\text{+5}\widehat{\text{j}}\text{-6}\widehat{\text{k}}$ at (2, 0, -3), about the point (2, -2, -2), is given by [NEET - 2018]

A)
$\text{-7}\widehat{\text{i}}\text{-8}\widehat{\text{j}}\text{-4}\widehat{\text{k}}$

B)
$\text{-4}\widehat{\text{i}}\text{-}\widehat{\text{j}}\text{-8}\widehat{\text{k}}$

C)
$\text{-8}\widehat{\text{i}}\text{-4}\widehat{\text{j}}\text{-7}\widehat{\text{k}}$

D)
$\text{-7}\widehat{\text{i}}\text{-4}\widehat{\text{j}}\text{-8}\widehat{\text{k}}$

• question_answer59) A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere? [NEET - 2018]

A)
Rotational kinetic energy

B)
Moment of inertia

C)
Angular velocity

D)
Angular momentum

• question_answer60) A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $\text{(}{{\text{K}}_{\text{t}}}\text{)}$ as well as rotational kinetic energy $\text{(}{{\text{K}}_{\text{r}}}\text{)}$ simultaneously. The ratio${{\text{K}}_{\text{t}}}\text{:(}{{\text{K}}_{\text{t}}}\text{+}{{\text{K}}_{\text{r}}}\text{)}$ for the sphere is                              [NEET - 2018]

A)
10 : 7

B)
5 : 7

C)
7 : 10

D)
(4) 2 : 5

• question_answer61) A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: $(g=10\text{ }m/{{s}^{2}})$               [NEET 2019]

A)

B)

C)
$\sqrt{10\text{ }}rad/s$

D)
$\frac{10}{2\pi }rad/s$

• question_answer62) A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it? [NEET 2019]

A)
2 J

B)
1 J

C)
3 J

D)
30 kJ

• question_answer63) A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after $2\pi$ revolutions is- [NEET 2019]

A)
$12\times {{10}^{4}}\text{ }Nm$

B)
$2\times {{10}^{6}}\text{ }Nm$

C)
$2\times {{10}^{6}}\text{ }Nm$

D)
$2\times {{10}^{3}}\text{ }Nm$

• question_answer64)  Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of:        [NEET 2020]

A)
50 cm

B)
67 cm

C)
80 cm

D)
33 cm