553 + Interview Questions in ROTATIONAL-MOTION IN GENERAL AWARENESS Page 9 InterviewSolution

401.	Moment of inertia of a uniform circular disc about a diameter is `I`. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be.A. `5l`B. `3l`C. `6l`D. `4l`
Answer» Correct Answer - c

Discussion

402.	A circular disc of radius `R` and thickness `R//6` has moment of inertia `I` about an axis passing through its centre and perpendicular to its plane. It is melted and recast into a solid sphere. The `M.I` of the sphere about its diameter as axis of rotation isA. IB. `(I)/(5)`C. `(I)/(10)`D. `(2I)/(8)`
Answer» Correct Answer - B `I_(d)=(MR^(2))/(2)`

Discussion

403.	A uniform disc of radius R lies in x-y plane with its centre at origin. Its moment of inertia about the axis x=2R and y=0 is equal to the moment of inertia about the axis y=d and z=0, where d is equal toA. `(4)/(3)R`B. `(sqrt17)/(2)R`C. `sqrt13R`D. `(sqrt15)/(2)R`
Answer» Correct Answer - B

Discussion

404.	A small pulley of radius 20 cm and moment of inertia `0.32 kg-m^(2)` is used to hang a 2 kg mass with the help of massless string. If the block is released, for no slipping condition find the acceleration of the block ( in `m//s^(2)`).
Answer» Correct Answer - 2

Discussion

405.	The moment of inertia of uniform circular disc about an axis passing through its centre is `6kgm^(2)` . Its M.I. about an axis perpendicular to its plane and just touching the rim will beA. `18kg m^(2)`B. `30kg m^(2)`C. `15 kg m^(2)`D. `3kg m^(2)`
Answer» Correct Answer - A `I_(c )=(MR^(2))/(2)= 6 kgm^(2)` `I_(t)=(3MR^(2))/(2)=3xx6=18`

Discussion

406.	If moment of inertia of a solid sphere of mass 5kg about its diameter is `50kg m^(2)` . Its moment of inertia about its tangent in kg `m^(2)` isA. 260B. 250C. 240D. 175
Answer» Correct Answer - D `I_(0)=I_(C )+Mh^(2)` `=50+5xx25=50xx125=175 kg m^(2)`.

Discussion

407.	Two spheres each mass M and radius R are connected with massless rod of length 2R . Then moment of inertia of the system about an axis passing through the centre of one of sphere and perpendicular to the rod will beA. `(21)/(5)MR^(2)`B. `(23)/(5)MR^(2)`C. `(22)/(5)MR^(2)`D. `(24)/(5)MR^(2)`
Answer» Correct Answer - D `I = (2)/(5)MR^(2)+(2)/(5)MR^(2)+M(2R)^(2)` `=(4)/(5)MR^(2)+4MR^(2)=(24)/(5)MR^(2)`

Discussion

408.	Three point masses, each of mass 2kg are placed at the corners of an equilateral triangle of side 2m. What is moment of inertia of this system about an axis along one side of a triangle?A. `2kg m^(2)`B. `4 kg m^(2)`C. `6 kg m^(2)`D. `8 kg m^(2)`
Answer» Correct Answer - B `I = (2)/(3)xx3xx(4)/(3)pixx27xx3xx3=648 pi "gm cm"^(2)`.

Discussion

409.	If temperature increases, the moment of inertia of a solid sphere about its diameterA. increasesB. decreasesC. remains unchangedD. becomes negative
Answer» Correct Answer - A

Discussion

410.	With the increase in temperate, moment of inertia of a solid sphere about the diameter.A. decreasesB. increasesC. does not changeD. none of these
Answer» Correct Answer - B

Discussion

411.	Moment of inertia of a solid sphere about its diameter is I . If that sphere is recast into 8 identical small spheres, then moment of inertia of such small sphere about its diameter isA. `I//8`B. `I//16`C. `I//24`D. `I//32`
Answer» Correct Answer - D `"M = 8 m " therefore m=(M)/(8)` Volume of big sphere = Volume of 8 spheres `(4pi)/(3)R^(3)=8xx(4pi)/(3)r^(3)` `R = 2 r` `therefore " " r = (R )/(2)` `I_(1)=(2)/(5)mr^(2)` `= (2)/(5)mr^(2)` `= (2)/(5)xx(M)/(8)xx((R )/(2))^(2)` `= (2)/(5)MR^(2)xx(1)/(8)xx(1)/(4)` `I_(1)=I xx(1)/(32)`.

Discussion

412.	The angular momentum of a body with mass (m) moment of inertia `(I)` and angular velocity `(omega)" rad"//s` is equal toA. `Iomega`B. `I omega^(2)`C. `I/omega`D. `1/omega^(2)`
Answer» Correct Answer - a

Discussion

413.	Moment of inertia of the earth about an axis passing through its centre of mass is (where R and `rho` are radius and density of the earth respectively).A. `(2//5)pi R^(5)rho`B. `(2//3)pi R^(5)rho`C. `(8//15)pi R^(5)rho`D. `(4//15)pi R^(5)rho`
Answer» Correct Answer - C `I=(2)/(5)MR^(2)=(2)/(5)rho VR^(2)` `=(2)/(5)rho (4 pi)/(3)R^(3)xx R^(2)= (8)/(15)rho pi R^(5)`

Discussion

414.	What is the moment of inertia os a solid sphere of radius 3 cm and density 3 `g//cm^(3)` about its diameter in C.G.S. system?A. `148pi`B. `388 pi`C. `138 pi`D. `216 pi`
Answer» Correct Answer - B `I = (2)/(5)MR^(2)` `= (2)/(5)xx3xx(4)/(3)pi xx 27xx3xx3xx = 388 pi "gm cm"^(2)`.

Discussion

415.	The surface density (mass/area) of a circular disc of radius a depends on the distance from the centre as `rho(r)=A+Br.` Find its moment of inertia about the line perpendicular to the plane of the disc through its centre.A. `pia^(2)(A/2 + (2a)/5)`BB. `pia^(4)(A/2 + (2B)/5)`C. `2pia^(3)(A/2+ (Ba)/5)`D. None of these
Answer» a) dm = `2pirdr(rho)` = (A+Br)(2pirdr)` `I = int_(0)^(a)dmr^(2)` = `(piAa^(4))/2+ (2piBa^(5))/5 = pia^(4)(A/2+(2a)/5B)`

Discussion

416.	If `rho` is density of the material of a sphere of radius R . Then its moment of inertia about its diameter isA. `(8pi)/(15)rhoR^(5)`B. `(4pi)/(3)rhoR^(5)`C. `(2pi)/(5)rhoR^(5)`D. `(4pi)/(3)rhoR^(4)`
Answer» Correct Answer - A `I=(2)/(5)MR^(2)=(2)/(5)rho vR^(2)` `=(2)/(5)rho (4pi)/(3)R^(3)R^(2)` `= (8pi)/(15)rho R^(5)`.

Discussion

417.	A body of moment of inertia of `3kgm^(2)` rotating with an angular velocity or 2rad//s has the same kinetic energy as a mass of 12kg moving with a velocity ofA. `1m//s`B. `2m//s`C. `4m//s`D. `8m//s`
Answer» Correct Answer - A `KE_("rot")=KE_(L)` `(1)/(2)I omega^(2)=(1)/(2) mv^(2)` `3xx4=12 v^(2)` `v^(2)=1` `v = 1`.

Discussion

418.	A solid sphere and hollow sphere of the same material have mass. Then moment of inertia about the diameter is more forA. Solid sphereB. Hollow sphereC. same for bothD. none
Answer» Correct Answer - B

Discussion

419.	The rotational kinetic energies of two flywheels are equal. If the ratio of their moments of inertia is 1 : 9 then the ratio of their angular momenta isA. `5 : 1`B. `1 : 2`C. `2 : 1`D. `1: 4`
Answer» Correct Answer - C `(1)/(2)I_(1)omega_(1)^(2)=(1)/(2)I_(2)omega_(2)^(2) rArr (omega_(1)^(2))/(omega_(2)^(2))=(I_(2))/(I_(1))` `rArr (omega_(1))/(omega_(2)) = sqrt((I_(2))/(I_(1)))=sqrt((9)/(1))= 3:1` `therefore (L_(1))/(L_(2))=(omega_(2))/(omega_(1))=(1)/(3) rArr L_(1) : L_(2)` `= 1:3`.

Discussion

420.	The rotational kinetic energy of two bodies of moment of inertia `9 kg m^(2)` and `1kg m^(2)` are same . The ratio of their angular momenta isA. `1:3`B. `1:9`C. `9:1`D. `3:1`
Answer» Correct Answer - D `K.E._(1)=K.E._(2)` `(1)/(2)L_(1)=(1)/(2)L_(2)` `therefore ((L_(1))/(L_(2)))^(2)=(I_(1))/(I_(2))` `(L_(1))/(L_(2))=sqrt((I_(1))/(I_(2)))=sqrt((9)/(1))=(3)/(1)`

Discussion

421.	A body of moment of inertia of `3 kg m^(2)` rotating with an angular velocity of 2 rad/s has the same kinetic energy as that that of mass 12 kg moving with a velocity ofA. 1 m/sB. 2 m/sC. 4 m/sD. 8 m/s
Answer» Correct Answer - A `(1)/(2)I omega^(2)=(1)/(2)m v^(2)` `therefore (1)/(2)xx3xx4=(1)/(2)xx12 v^(2)` `therefore " " v^(2)=1 " " v =1 m//s`.

Discussion

422.	A wheel 2 kg having practically all the mass concentrated along the circumference of a circle of radius 20 cm is rotating on its axis with angular velocity of 100 rad/s, then the rotational kinetic energy of wheel isA. 4 JB. 70 JC. 400 JD. 800 J
Answer» Correct Answer - C `KE = (1)/(2) I omega^(2)`

Discussion

423.	There are two identical spherical balls of same material one being solid and the other being hollow. Then they can be distinguished byA. spinning them by applying rqual torquesB. rolling them down on the same inclined planeC. determining their moments of inertiaD. any one of the three method mentioned above
Answer» Correct Answer - D

Discussion

424.	Two rigid bodies `A` and `B` rotate with angular momenta `L_(A)` and `L_(B)` respectively. The moments of inertia of `A` and `B` about the axes of rotation are `I_(A)` and `I_(B)` respectively. If `I_(A)=I_(B)//4` and `L_(A)=5L_(B)`, then the ratio of rotational kinetic energy `K_(A)` of `A` to the rotational kinetic energy `K_(B)` of `B` is given byA. `25//4`B. `5//4`C. `1//4`D. 100
Answer» Correct Answer - D `(E_(1))/(E_(2))=(L_(1)^(2))/(L_(2)^(2))xx(I_(2))/(I_(1))=25xx4=(100)/(1)`.

Discussion

425.	Locus of all the points in a plane on which the moment of inertia about all mutually parallel axes of a rigid body is same throughout isA. a straight lineB. a circleC. a parabolaD. an ellipse
Answer» Correct Answer - B

Discussion

426.	A man stands at the centre of turn table and the turn table is rotating with certain angular velocity. If he walks towards rim of the turn table, thenA. moment of inertia of the system decreasesB. angular momentum of system increasesC. angular velocity of the system increasesD. kinetic energy of the system decreases
Answer» Correct Answer - D

Discussion

427.	Two rigid bodies have same moment of inertia about there axes of symmetry. Then which will have more kinetic energy ?A. Body having greater angular momentumB. Body having smaller angular momentumC. Both will have same kinetic energyD. Can not decided
Answer» Correct Answer - A

Discussion

428.	If polar ice caps melt, then the time duration of one dayA. increasesB. decreasesC. becomes zeroD. remains constant
Answer» Correct Answer - B

Discussion

429.	If polar ice caps melt, then the time duration of one dayA. increasesB. decreasesC. some times decreases, some times increasesD. remains constant
Answer» Correct Answer - A

Discussion

430.	A and B are two identical rings released from the top of an inclined plane . A slides down and B rolls down. Then which reaches the bottom first ? A. AB. BC. both in same timeD. none of these
Answer» Correct Answer - A

Discussion

431.	A solid cylinder rolls down an inclined plane of height `3m` and reaches the bottom of plane with angular velocity of `2sqrt2 rad//s`. The radius of cylinder must be [take `g=10m//s^(2)`]A. `5 cm`B. `0.5 cm`C. `sqrt10 cm`D. `sqrt5 m`
Answer» `v=sqrt((2gh)/(1+k^(2)//R^(2)))=sqrt((2gh)/(1+(1//2)))=sqrt((4gh)/(3))=sqrt((4xx10xx3)/(3))` `2sqrt10` `omega=(v)/(R )implies R=(v)/(omega)=(2sqrt10)/(2sqrt2)=sqrt5m`

Discussion

432.	A solid sphere a hollow sphere and a disc all having same mass and radius, are placed at the top of a moth incline and released. Least time will be taken in reaching the bottom byA. the solid sphereB. the hollow sphereC. the discD. all will take the same time
Answer» On smooth incline, no rotation, only sliding

Discussion

433.	A uniform hemisphere placed on an incline is on verge of sliding. The coefficient of friction between the hemisphere and the incline is `mu = 0.3`. Find the angle `phi` that the circular base of the hemisphere makes with the horizontal. Given `sin (tan^(-1) 0.3) cong 0.29 " and "sin^(-1) (0.77) cong 50^(@)`
Answer» Correct Answer - `50^(@)`

Discussion

434.	A solid cylinder of mass 2kg rolls down (pure rolling) an inclined plane from a height of 4m. Its rotational kinetic energy, when its reaches the foot of the plane is (Take g=10m`s^(-2))`A. 20 JB. 40 JC. `80/3`JD. 80 J
Answer» c) At foot of the plane, For rotational motion about CM `2Tr = 1/2Mr^(2)alpha` Where, r = radius of cylinder `rArr 2T = 1/2Ma`…………….(ii) `From Eqs. (i) and (ii), we get `a = 2/3g` and `T=(mg)/6` Now, from equation of motion ,`v^(2) = u^(2) + 2gh`, we get `v^(2) = 2(2/3g) h rArr v= sqrt((4gh)/3)` `mgh = 1/2 komega^(2) + 1/2mu^(2)` `80 = 3/4mu^(2)` `therefore` Rotational KE = 1/2lomega^(2)` `=1/4 mu^(2) = 1/4 xx (80 xx4)/3 = 80/3` J

Discussion

435.	A solid sphere, a ring and a disc all having same mass and radius are placed at the top of an incline and released. The friction coefficient between the objects and the incline are same but not sufficient to allow pure rolling. Least time will be taken in reaching the bottom byA. the solid sphereB. the ringC. the discD. all will take the same time
Answer» Correct Answer - D

Discussion

436.	A wheel of radius R=1 m rolls on ground with uniform velocity v=2 m/s . Calculate the relative acceleration of topmost point of wheel with respect to bottom most point (in `m//s^(2)`).
Answer» Correct Answer - 8

Discussion

437.	A wheel of radius R rolls on the ground with a uniform velocity v. The relative acceleration of topmost point of the wheel with respect to the bottommost point is:A. `(v^(2))/(R)`B. `(2v^(2))/(R)`C. `(v^(2))/(2R)`D. `(4v^(2))/(R)`
Answer» Correct Answer - B

Discussion

438.	If the radius of the earth contracts to half of its present value without change in its mass, what will be the new duration of the day?A. 48hB. 24hC. 12hD. 6h
Answer» Correct Answer - D `T_(2)=24 n^(2)`

Discussion

439.	Match the following .
Answer» Correct Answer - (A)Q,T,U(B)Q,T,U(C)Q,T,U

Discussion

440.	A particle of mass `m` is rotating in a plane in circular path of radius `r`. Its angular momentum is `L`. The centripetal force acting on the particle isA. `L^(2)/MR^(3)`B. `ML^(2)/R_(3)`C. `MR^(3)/L^(2)`D. `L^(2)/2MR^(3)`
Answer» Correct Answer - A `CF = MR omega^(2)=(MR^(2)omega^(2))/(R )`

Discussion

441.	Length AB in the figure shown in 5 m. The body is released from A. Friction is sufficient for pure rolling to take place. The maximum time which anybody (which can roll) can take to reach the bottom isA. 8 sB. 6sC. 2 sD. 4 s
Answer» Correct Answer - C

Discussion

442.	Length AB in the figure shown in 5 m. The body is released from A. Friction is sufficient for pure rolling to take place. In the above case suppose we have four bodies ring, disc, solid sphere and hollow sphere. The angle `theta` is now gradually increased. Which body will start slipping very fast. All the bodies have same mass and radius. Coefficient of friction is also same ?A. RingB. DiscC. Solid sphereD. Hollow sphere
Answer» Correct Answer - A

Discussion

443.	A wheel of radius R=2m performs pure rolling on a rough horizontal surface with speed v=10 m/s . In the figure shown, angle `theta` is angular position of point P on wheel reaches the maximum height from ground. Find the value of `"sec"theta` (take `g=10 m//s^(2)`).
Answer» Correct Answer - 5

Discussion

444.	A circular disc P of radius R is made from an iron plate of thickness t and another disc Q of radius 2R is made from an iron plate of thickness `(t)/(2)`. The relation between their moments of inertia `I_(p)` and `I_(Q)` about their natural axes isA. `I_(Q)=4I_(P)`B. `I_(P)=8I_(Q)`C. `I_(P)=4I_(Q)`D. `I_(Q)=8I_(P)`
Answer» Correct Answer - D `I_(P)=(MR^(2))/(2)` `(((pi R^(2))t)rho(R^(2)))/(2)=(pi t rho R^(4))/(2)` `I_(Q)=(MR^(2))/(2)` `=((pi(2R)^(2)(t//2))rho(2R)^(2))/(2)` `= (pi t rho(8 R^(4)))/(2)=8I_(P)`.

Discussion

445.	A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness `t//4`. The relation between the moments of inertia `I_(A)` and `I_(B)` is (about an axis passing through centre and perpendicular to the disc)A. `l_(A)gtl_(B)`B. `l_(A)=l_(B)`C. `l_(A)ltl_(B)`D. depends on the actul values of t and r
Answer» Correct Answer - C

Discussion

446.	A circular disc `A` of radius `r` is made from an iron plate of thickness `t` and another circular disc `B` of radius `4r` is made from an iron plate of thickness `t//4`. Equal torques act on the discs `A` and `B`, initially both being at rest. At a later instant, the linear speeds of a point on the rim of `A` and another point on the rim of `B` are `v_(A)` and `v_(B)`, respectively. We haveA. `v_(A) gt v_(B)`B. `v_(A) = v_(B)`C. `v_(A) lt v_(B)`D. The relation depends on the actual magnitude of the torques.
Answer» `m_(A)=rhoxxpir^(2)t=m` `m_(B)=rhoxxpi(4r)^(2)(t)/(4)=4m` `I_(A)=(1)/(2)mr^(2)=I,I_(B)=(1)/(2)xx4m(4r)^(2)=64I` `alpha_(A)=(tau)/(I)=alpha_(0), alpha_(B)=(tau)/(64I), omega=0+alphat` `v_(A)=omega_(A)r=alpha_(0)rt` `v_(B)=omega_(B)4r=(alpha_(0)rt)/(16)`

Discussion

447.	A uniform cylindrical body of radius r has a conical nose. The length of the cylindrical and conical parts are `4r` and `3r` respectively. Mass of the conical part is M. The body rests on a horizontal surface as shown. A ring of radius `(r)/(2)` is to be tightly fitted on the nose of the body. What is maximum permissible mass of the ring so that the body does not topple?
Answer» Correct Answer - `(29)/(6) M`

Discussion

448.	A particle of mass m and velocity `v_(0)` is fired at a solid cylinder of mass M and radius R. The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through the centre of mass. The line of motion of the particle is perpendicular to the axle and at a distance d, less than R, from the centre and the particle sticks to the surface of hte cylinder, thenA. Angular speed of the system just after the particle stick is `(2 mv_(0)d)/(R^(2)(M+2m))`B. Mechanical energy is conservedC. angular speed of the system just after the particle sticks is `( mv_(0)d)/(R^(2)(M+2m))`D. Mechanical energy is not conserved
Answer» Correct Answer - A::D

Discussion

449.	If a ring, disc, hollow sphere and solid sphere rolling horizontally without slipping with the same velocity on a surface, then translational kinetic energy is more forA. ringB. discC. sphereD. we can not say
Answer» Correct Answer - D

Discussion

450.	A solid cylinder of mass 0.1 kg having radius 0.2m rolls down an inclined plane of height 0.6m without slipping. The linear velocity the cylinder at the bottom of the inclined plane isA. `28 ms^(-1)`B. `2.8 ms^(-1)`C. `280 ms^(-1)`D. `0.28 ms^(-1)`
Answer» Correct Answer - B According to the law of conservation of energy. `(3)/(4)mv^(2)= mgh rArr v = sqrt((4gh)/(3)) = sqrt((4(9.8)(0.6))/(3))` `= (28)/(10)= 2.8 ms^(-1)`.

Discussion

Explore topic-wise InterviewSolutions in .

Moment of inertia of a uniform circular disc about a diameter is `I`. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be.A. `5l`B. `3l`C. `6l`D. `4l`

A uniform disc of radius R lies in x-y plane with its centre at origin. Its moment of inertia about the axis x=2R and y=0 is equal to the moment of inertia about the axis y=d and z=0, where d is equal toA. `(4)/(3)R`B. `(sqrt17)/(2)R`C. `sqrt13R`D. `(sqrt15)/(2)R`

A small pulley of radius 20 cm and moment of inertia `0.32 kg-m^(2)` is used to hang a 2 kg mass with the help of massless string. If the block is released, for no slipping condition find the acceleration of the block ( in `m//s^(2)`).

The moment of inertia of uniform circular disc about an axis passing through its centre is `6kgm^(2)` . Its M.I. about an axis perpendicular to its plane and just touching the rim will beA. `18kg m^(2)`B. `30kg m^(2)`C. `15 kg m^(2)`D. `3kg m^(2)`

If moment of inertia of a solid sphere of mass 5kg about its diameter is `50kg m^(2)` . Its moment of inertia about its tangent in kg `m^(2)` isA. 260B. 250C. 240D. 175

Two spheres each mass M and radius R are connected with massless rod of length 2R . Then moment of inertia of the system about an axis passing through the centre of one of sphere and perpendicular to the rod will beA. `(21)/(5)MR^(2)`B. `(23)/(5)MR^(2)`C. `(22)/(5)MR^(2)`D. `(24)/(5)MR^(2)`

Three point masses, each of mass 2kg are placed at the corners of an equilateral triangle of side 2m. What is moment of inertia of this system about an axis along one side of a triangle?A. `2kg m^(2)`B. `4 kg m^(2)`C. `6 kg m^(2)`D. `8 kg m^(2)`

If temperature increases, the moment of inertia of a solid sphere about its diameterA. increasesB. decreasesC. remains unchangedD. becomes negative

With the increase in temperate, moment of inertia of a solid sphere about the diameter.A. decreasesB. increasesC. does not changeD. none of these

Moment of inertia of a solid sphere about its diameter is I . If that sphere is recast into 8 identical small spheres, then moment of inertia of such small sphere about its diameter isA. `I//8`B. `I//16`C. `I//24`D. `I//32`

The angular momentum of a body with mass (m) moment of inertia `(I)` and angular velocity `(omega)" rad"//s` is equal toA. `Iomega`B. `I omega^(2)`C. `I/omega`D. `1/omega^(2)`

Moment of inertia of the earth about an axis passing through its centre of mass is (where R and `rho` are radius and density of the earth respectively).A. `(2//5)pi R^(5)rho`B. `(2//3)pi R^(5)rho`C. `(8//15)pi R^(5)rho`D. `(4//15)pi R^(5)rho`

What is the moment of inertia os a solid sphere of radius 3 cm and density 3 `g//cm^(3)` about its diameter in C.G.S. system?A. `148pi`B. `388 pi`C. `138 pi`D. `216 pi`

If `rho` is density of the material of a sphere of radius R . Then its moment of inertia about its diameter isA. `(8pi)/(15)rhoR^(5)`B. `(4pi)/(3)rhoR^(5)`C. `(2pi)/(5)rhoR^(5)`D. `(4pi)/(3)rhoR^(4)`

A body of moment of inertia of `3kgm^(2)` rotating with an angular velocity or 2rad//s has the same kinetic energy as a mass of 12kg moving with a velocity ofA. `1m//s`B. `2m//s`C. `4m//s`D. `8m//s`

A solid sphere and hollow sphere of the same material have mass. Then moment of inertia about the diameter is more forA. Solid sphereB. Hollow sphereC. same for bothD. none

The rotational kinetic energies of two flywheels are equal. If the ratio of their moments of inertia is 1 : 9 then the ratio of their angular momenta isA. `5 : 1`B. `1 : 2`C. `2 : 1`D. `1: 4`

The rotational kinetic energy of two bodies of moment of inertia `9 kg m^(2)` and `1kg m^(2)` are same . The ratio of their angular momenta isA. `1:3`B. `1:9`C. `9:1`D. `3:1`

A body of moment of inertia of `3 kg m^(2)` rotating with an angular velocity of 2 rad/s has the same kinetic energy as that that of mass 12 kg moving with a velocity ofA. 1 m/sB. 2 m/sC. 4 m/sD. 8 m/s

A wheel 2 kg having practically all the mass concentrated along the circumference of a circle of radius 20 cm is rotating on its axis with angular velocity of 100 rad/s, then the rotational kinetic energy of wheel isA. 4 JB. 70 JC. 400 JD. 800 J

Locus of all the points in a plane on which the moment of inertia about all mutually parallel axes of a rigid body is same throughout isA. a straight lineB. a circleC. a parabolaD. an ellipse

Two rigid bodies have same moment of inertia about there axes of symmetry. Then which will have more kinetic energy ?A. Body having greater angular momentumB. Body having smaller angular momentumC. Both will have same kinetic energyD. Can not decided

If polar ice caps melt, then the time duration of one dayA. increasesB. decreasesC. becomes zeroD. remains constant

If polar ice caps melt, then the time duration of one dayA. increasesB. decreasesC. some times decreases, some times increasesD. remains constant

A and B are two identical rings released from the top of an inclined plane . A slides down and B rolls down. Then which reaches the bottom first ? A. AB. BC. both in same timeD. none of these

A solid cylinder rolls down an inclined plane of height `3m` and reaches the bottom of plane with angular velocity of `2sqrt2 rad//s`. The radius of cylinder must be [take `g=10m//s^(2)`]A. `5 cm`B. `0.5 cm`C. `sqrt10 cm`D. `sqrt5 m`

A solid sphere a hollow sphere and a disc all having same mass and radius, are placed at the top of a moth incline and released. Least time will be taken in reaching the bottom byA. the solid sphereB. the hollow sphereC. the discD. all will take the same time

A solid cylinder of mass 2kg rolls down (pure rolling) an inclined plane from a height of 4m. Its rotational kinetic energy, when its reaches the foot of the plane is (Take g=10m`s^(-2))`A. 20 JB. 40 JC. `80/3`JD. 80 J

A wheel of radius R=1 m rolls on ground with uniform velocity v=2 m/s . Calculate the relative acceleration of topmost point of wheel with respect to bottom most point (in `m//s^(2)`).

A wheel of radius R rolls on the ground with a uniform velocity v. The relative acceleration of topmost point of the wheel with respect to the bottommost point is:A. `(v^(2))/(R)`B. `(2v^(2))/(R)`C. `(v^(2))/(2R)`D. `(4v^(2))/(R)`

If the radius of the earth contracts to half of its present value without change in its mass, what will be the new duration of the day?A. 48hB. 24hC. 12hD. 6h

Match the following .

A particle of mass `m` is rotating in a plane in circular path of radius `r`. Its angular momentum is `L`. The centripetal force acting on the particle isA. `L^(2)/MR^(3)`B. `ML^(2)/R_(3)`C. `MR^(3)/L^(2)`D. `L^(2)/2MR^(3)`

Length AB in the figure shown in 5 m. The body is released from A. Friction is sufficient for pure rolling to take place. The maximum time which anybody (which can roll) can take to reach the bottom isA. 8 sB. 6sC. 2 sD. 4 s

A wheel of radius R=2m performs pure rolling on a rough horizontal surface with speed v=10 m/s . In the figure shown, angle `theta` is angular position of point P on wheel reaches the maximum height from ground. Find the value of `"sec"theta` (take `g=10 m//s^(2)`).

If a ring, disc, hollow sphere and solid sphere rolling horizontally without slipping with the same velocity on a surface, then translational kinetic energy is more forA. ringB. discC. sphereD. we can not say

A solid cylinder of mass 0.1 kg having radius 0.2m rolls down an inclined plane of height 0.6m without slipping. The linear velocity the cylinder at the bottom of the inclined plane isA. `28 ms^(-1)`B. `2.8 ms^(-1)`C. `280 ms^(-1)`D. `0.28 ms^(-1)`