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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.
| 451. |
A cylindrical ring is rolling without slipping. The ration of rotational and translational kinetic energies isA. `0.25`B. 0.5C. 1D. 1.5 |
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Answer» Correct Answer - C `KE_("translational")=(1)/(2)mv^(2)` `KE_("rotational")=(1)/(2)l omega^(2)` `=(1)/(2)(mr^(2))omega^(2)=(1)/(2)mv^(2)` `(KE_("tans"))/(KE_("rot"))=1`. |
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| 452. |
In the figure shown, the plank is being pulled to the right with a constant speed `v`. If the cylinder does not slip then: .A. the speed of the centre of the mass of the cylinder is 2 VB. the speed of the centre of the mass of the cylinder is vC. The angular velocity of the cylinder is `v//R`D. The angular velocity of the cylinder is zero |
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Answer» Correct Answer - C |
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| 453. |
A spool of mass `M` and radius `2R` lies on an inclined plane as shown in the figure. A light thread is wound around the connecting tube of the spool and its free end carries a weight of mass `m`. The value of `m` so that system is in equilibrium is A. `2M sin alpha`B. `M sin alpha`C. `2M tan alpha`D. `M cos alpha` |
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Answer» Correct Answer - A |
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| 454. |
In the above problem, direction of friction force isA. towards left if `F_(1)` is appliedB. towards left if `F_(2)` is appliedC. towards right if `F_(3)` is appliedD. may be right or left or friction may be zero if `F_(4)` is applied |
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Answer» Correct Answer - A::B::D |
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| 455. |
A spool of wire rests on a horizontal surface as shown in figure. As the wire is pulled, the spool does not slip at contact point P. On separate trials, each one of the force `F_(1),F_(2),F_(3) " and " F_(4)` is applied to the spool. For each one of these forces the spool. A. will rotate anticlockwise if `F_(1)` is appliedB. will not rotate if `F_(2)` is appliedC. will rotate anticlockwise if `F_(3)` is appliedD. will rotate clockwise if `F_(4)` is applied |
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Answer» Correct Answer - B::C |
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| 456. |
A hollow cylinder open at both ends slides without rotating, and then rolls without slipping with the same speed. The ratio of the kinetic energy in the two cases is (taken in order)A. `1 : 1`B. `1 : 2`C. `2 : 1`D. `1 : 4` |
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Answer» Correct Answer - B `KE_(1)=(1)/(2)mv^(2)` `KE_(2)=(1)/(2)mv^(2)+(1)/(2)l omega^(2)` `= (1)/(2)mv^(2)+(1)/(2)(mr^(2))((v^(2))/(r^(2)))=mv^(2)` `rArr (KE_(1))/(KE_(2))= +((1)/(2)mv^(2))/(mv^(2))=(1)/(2)= 1:2`. |
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| 457. |
A hollow sphere rolls on a horozontal surface without slipping. Then percentages of rotational kinetic energy in total energy isA. `60%`B. `40%`C. `72%`D. `28%` |
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Answer» Correct Answer - B `(KE_("rot"))/(KE_("roll"))=(K^(2)//R^(2))/(1+K^(2)//R^(2))` `=((2)/(3))/(1+(2)/(3))=((2)/(3))/((7)/(3))=(2)/(7)=0.28=28%`. |
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| 458. |
A solid uniform disc of mass `m` rolls without slipping down a fixed inclined plank with an acceleration a. The frictional force on the disc due to surface of the plane isA. 2 maB. `(3)/(2)` maC. maD. `(1)/(2)` ma |
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Answer» Correct Answer - D |
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| 459. |
When a solid sphere rolls without slipping down an inclined plane making an angle `theta` with the horizontal, the acceleration of its centre of mass is `a`. If the same sphere slides without friction, its.A. `(7//2)` aB. `(5//7)` aC. `(7//5)` aD. `(5//2)` a |
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Answer» Correct Answer - C |
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| 460. |
In a circus, a motor cyclist goes round a vertical circle inside a spherical cage of radius `4.5 m`. Calculate the minimum speed of the motor cycle inside the cage. |
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Answer» Correct Answer - `6.64 ms^(-1)` |
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| 461. |
A motor cyclist goes round a circular race course of diameter 320 m at `144 km h^(-1)`. How far from the vertical must he lean inwards to keep his balance? Take `g = 10 ms^(-2)`. |
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Answer» Correct Answer - `45^(@)` |
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| 462. |
A ball rolls down an inclined plane from a height and then goes round a vertical circle of radius 1m. What should be the height of the inclined plane so that the ball is able to go round the circle without leaving the track? |
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Answer» Correct Answer - 2.5 m |
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| 463. |
The railway bridge over a canal is in the form of an arc of a circle of radius 20m. What is the minimum speed with which a car can cross the bridge without leaving contact with the ground at the highest point ? Take `g = 9.8 ms^(-2)` |
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Answer» Correct Answer - `14 ms^(-1)` |
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| 464. |
A solid sphere of mass M and radius R is covered with a thin shell of mass M. There is no friction between the inner wall of the shell and the sphere. The ball is released from rest, and then it rolls without slipping down an incline that is inclined at an angle `theta` to the horizontal. Find the acceleration of the ball. |
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Answer» Correct Answer - `a = (3 g sin theta)/(4) |
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| 465. |
A thread is tightly wrapped on two pulleys as shown in figure. Both the pulleys are uniform disc with upper one having mass M and radius R being free to rotate about its central horizontal axis. The lower pulley has mass m and radius r and it is released from rest. It spins and falls down. At the instant of release a small mark (A) was at the top point of the lower pulley. (a) After what minimum time `(t_(0))` the mark will again be at the top of the lower pulley? (b) Find acceleration of the mark at time `t_(0)`. (c) Is there any difference in magnitude of acceleration of the mark and that of a point located on the circumference at diametrically opposite end of the pulley. |
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Answer» Correct Answer - (a) `t_(0) = sqrt((2pi (2m + 3M)r)/(Mg))` (b) `a = (2g)/(2m + 3M)n sqrt(m^(2) + (4 pi M + M + m)^(2))` (c) yes |
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| 466. |
A light thread is wrapped tightly a few turns around a disc P of mass M. One end of the thread is fixed to the ceiling at B. The other end of the thread is passed over a mass less pulley (Q) and carries a block of mass M. All segment of the thread (apart from that on the pulley and disc) are vertical when the system is released. Find the acceleration of block A. On which object – the block A or the ceiling at B – does the thread exert more force ? |
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Answer» Correct Answer - `(4g)/(11)`; Thread exerts more force on A |
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| 467. |
A light thread has been tightly wrapped around a disc of mass M and radius R. The disc has been placed on a smooth table, lying flat as shown. The other end of the string has been attached to a mass `m` as shown. The system is released from rest. If `m = M`, which point of the disc will have zero acceleration, immediately after the system is released? |
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Answer» Correct Answer - A point at a distance `(R)/(2)` from centre |
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| 468. |
In the figure shown, the light thread is tightly wrapped on the cylinder and masses of plank and cylinder are same each equal to `m`. An external agent begins to pull the plank to the right with a constant force F. The friction between the plank and the cylinder is large enough to prevent slipping. Assume that the length of the plank is quite large and the cylinder does not fall off it for the time duration concerned. (a) Find the acceleration of the cylinder. (Hint : don’t write any equations) (b) Find the kinetic energy of the system after time `t`. |
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Answer» Correct Answer - (a) Zero (b) `(F^(2) t^(2))/(3m)` |
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| 469. |
The pulley of radius R can rotate freely about its axle as shown in the figure. A thread is tightly wrapped around the pulley and its free end carries a block of mass `m`. When the block is at a height `h` above the ground the system is released (i.e., the pulley is made free to rotate & the block is allowed to fall) and at the same instant the axle is moved up keeping it horizontal all the time. When the block hits the floor the axle has gone up by a distance `2h`. Find the angle by which the pulley must have rotated by this time. |
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Answer» Correct Answer - `(3h)/(R)` |
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| 470. |
A uniform disc shaped pulley is free to rotate about a horizontal axis passing through the centre of the pulley. A light thread is tightly wrapped over it and supports a mass m at one of its end. A small particle of mass `m_(0) = 2m` is stuck at the lowest point of the disc and the system is released from rest. Will the particle of mass `m_(0)` climb to the top of the pulley? |
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Answer» Correct Answer - No |
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| 471. |
A mass less string is wrapped around a uniform disc of mass m and radius `r`. The string passes over a mass less pulley and is tied to a block of mass M at its other end (see figure). The system is released from rest. Assume that the string does not slip with respect to the disc. (a) Find the acceleration of the block for the case `M = m` (b) Find `(M)/(m)` for which the block can accelerate upwards. |
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Answer» Correct Answer - (a) `(g)/(2)` (b) `(M)/(m) lt (1)/(3)` |
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| 472. |
A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Force of friction acting on the cylinder isA. `(2mg)/(3)`B. `(3mg)/(2)`C. `(mg)/(3)`D. `(mg)/(6)` |
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Answer» Correct Answer - D |
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| 473. |
A uniform solid cylinder of mass m and radius 2R rests on a horizontal table. A string attached to it passes over a pulley (disc) of mass m and radius R that is mounted on a fricitonaless axle through its centre . A block of mass m is suspended from the free end of the spring . The string does not slip over the pulley surface and the cylinder rolls without slipping on the table. Acceleration of the block isA. `(g)/(3)`B. `(3g)/(4)`C. `(2g)/(3)`D. `(5g)/(7)` |
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Answer» Correct Answer - A |
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| 474. |
A light rod of length `l` has two masses `m_1` and `m_2` attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is.A. `(m_(1)m_(2))/(m_(1)+m_(2)) l^(2)`B. `(m_(1)+m_(2))/(m_(1)m_(2)) l^(2)`C. `(m_(1)+m_(2))l^(2)`D. `sqrt(m_(1)m_(2))l^(2)` |
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Answer» Correct Answer - a |
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| 475. |
A dancer spins about himself with an angular speed `omega`, with his arms extended. When he draws his hands in, his moment of inertia reduces by 40% . Then his angular velocity would beA. `3omega//4`B. `4omega//5`C. `5omega//4`D. `5omega//3` |
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Answer» Correct Answer - D `w_(2)=(I omega xx 100)/(60I)=(5omega)/(3)`. |
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| 476. |
A boy stands on a freely rotating platform with his arms extended. His rotation speed is 0.3 rev/s, when he draws in, his speed increases to 0.5 rev/s, then the ratio of his moment of inertia in these two cases will beA. `3 : 5`B. `5 : 3`C. `9 : 25`D. `25 : 9` |
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Answer» Correct Answer - B `I_(1)omega_(1)=I_(2)omega_(2)` `KE_(2)=(1)/(2)I omega^(2)` |
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| 477. |
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?A. Moment of inertiaB. Angular momentumC. Angular velocityD. Rotational kinetic energy |
| Answer» No external torque, angular momentum is conserved. | |
| 478. |
A uniform horizontal circular platform of mass `200 kg` is rotating at 10 rpm about a vertical axis passing through its center. A boy of mass `50 kg` is standing at its edge. If the boy moves to the center of the platform, the frequency of rotation would becomeA. `7.5` rpmB. `12.5` rpmC. 15 rpmD. 20 rpm |
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Answer» `[(1)/(2)(200)r^(2)+50r^(2)](10)=(1)/(2)(200)r^(2)omega` `omega=15rp m` |
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| 479. |
Two solid discs of radii `r` and `2r` roll from the top of an inclined plane without slipping. ThenA. The bigger disc will reach the horizontal level firstB. The smaller disc will reach the horizontal level firstC. The time difference or reaching of the discs at the horizontal level will depend on the inclination of the planeD. Both the discs will reach at the same time |
| Answer» The factor `((k^(2))/(R^(2)))=(1)/(2)`, for all discs | |
| 480. |
A hollow sphere (`i`) rolls and (`ii`) slides down an inclined plane. The ratio of the accelerations in the two cases isA. `3 : 4`B. `3 : 5`C. `2 : 3`D. `5 : 7` |
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Answer» `a_(1)=(gsin theta)/(1+k^(2)//R^(2))=(g sin 30^(@))/(1+2//3)=(3 g sin theta)/(5)` `a_(2)= g sin theta` `(a_(1))/(a_(2))=(3)/(5)` |
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| 481. |
The point masses of 0.3 kg, 0.2 kg and 0.1 kg are placed at the corner of a right angles `Delta ABC`, as shown in Fig. 8.49. find the moment of inertia of the system (i) about an axis through A and perpendicular to the plane of the diagram and (ii) about an axis along BC. |
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Answer» Correct Answer - (i) `0.043 kg m^(2)` (ii) `0.027 kg m^(2)` |
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| 482. |
A uniform rod of length l and mass m is suspended from one end by inextensible string and other end less lies on smooth ground. The angle made by the rod with vertical is `theta="sin"^(-1)(1//sqrt(3))`. If `N_(1)` and `N_(2)` represent the contact force from ground on rod just before and just after cutting the string then the ratio of `N_(1)//N_(2)` is 0.25 x. Find the value of x. |
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Answer» Correct Answer - 3 |
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| 483. |
A uniform rod BC with length a is attached to a light string AC. End A of the string is fixed to the ceiling and the end B of the rod is on a smooth horizontal surface. B is exactly below point A and length AB is `b (a lt b lt 2a)`. The system is released from rest and the rod begins to slide. Find the speed of the centre of the rod when the string becomes vertical. |
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Answer» Correct Answer - `v = sqrt((s(a-(b)/(2)))` |
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| 484. |
A small body is attached to one end of a string is revolved around a rod so that the string winds upon the rod and get shortend. The quantity which is conserved isA. angular momentumB. linear momentumC. kinetic energyD. potential enegy |
| Answer» Correct Answer - A | |
| 485. |
A ring is rolling, without slipping on a horizontal surface with constant velocity. Speed of point A (at the top) is `v_(A)`. After an interval `T`, the speed of point A again becomes `v_(A)`. During what fraction of the interval T speed of point A was greater than `(sqrt3)/(2) v_(A)` |
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Answer» Correct Answer - `(1)/(3)` |
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| 486. |
A ring mass `m` and radius `R` has three particle attached to the ring as shown in the figure. The centre of the centre `v_(0)`. Find the kinetic energy of the system. (Slipping is absent). .A. `6mv_(0)^(2)`B. `12mv_(0)^(2)`C. `4mv_(0)^(2)`D. `8mv_(0)^(2)` |
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Answer» Correct Answer - A |
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| 487. |
A solid sphere and a disc of same radii are falling along an inclined plane without slip. One reaches earlier than the other due to.A. sizesB. frictional forceC. moment of inertiaD. radius of gyration |
| Answer» Correct Answer - D | |
| 488. |
A body comes and sits suddenly on a circular rotating table the quantity which conserved isA. angular velocityB. angular momentumC. linear momentumD. angular acceleration |
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Answer» Correct Answer - B As no torque is exerted the boy. |
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| 489. |
The angular momentum of two circular discs is same. The mass of the first disc is more than second disc then the rotational K.E. is more forA. lighter discB. heavier discC. both will have same rotational K.E.D. depends upon shape |
| Answer» Correct Answer - A | |
| 490. |
A particle of mass `m` moves along line `PC` with velocity `v` as shown. What is the angular momentum of the particle about `O`? A. `mvL`B. `mvl`C. `mvr`D. `zero` |
| Answer» Angular momentum `=` linear momentum `xx` lever arm `=mvl` | |
| 491. |
Analogue of a force in a rotational motion, isA. weightB. torqueC. angular momentumD. moment of inertia |
| Answer» Correct Answer - B | |
| 492. |
The dimensions of the radius of gyration areA. `[L^(1)M^(1)T^(0)]`B. `[L^(1)M^(0)T^(0)]`C. `[L^(1)M^(0)T^(1)]`D. `[L^(1)M^(2)T^(0)]` |
| Answer» Correct Answer - B | |
| 493. |
The M.I. of a wheel of mass 8 kg and radius of gyration 25 cm isA. `5 kg m^(2)`B. `1.5 kg m^(2)`C. `2.5 kg m^(2)`D. `0.5 kg m^(2)` |
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Answer» Correct Answer - D `I = mK^(2) = 8xx(0.25)^(2)= 8xx((1)/(4))^(2)` `= 8xx(1)/(16)=(1)/(2)=0.5 kg m^(2)` `I = 0.5 kg m^(2)` |
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| 494. |
A body is rolling down an inclined plane. If kinetic energy of rotation is `40 %` of kinetic energy in translatory start then the body is a.A. discB. Hollow sphereC. RingD. Solid sphere |
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Answer» Correct Answer - D `(K^(2))/(R^(2))=0.4`, for solid sphere |
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| 495. |
Dimensions of moment of inertia areA. `[L^(2)M^(2)T^(-1)]`B. `[L^(2)MT^(0)]`C. `[LMT^(-1)]`D. `[L^(2)M T^(-2)]` |
| Answer» Correct Answer - B | |
| 496. |
A cylinder full of water is rotating about its own axis with uniform angular velocity `omega`. Then the shape of free surface of water will beA. parabolaB. ellipticalC. circularD. spherical |
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Answer» Correct Answer - A Bacause difference in centrifugal force. (`F = mr omega^(2)` which is propontional to r). |
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| 497. |
In an orbital motion, the angular momentum vector is :A. along the radius vectorB. parallel to the linear momentumC. in the orbital planeD. perpendicular to the orbital plane |
| Answer» Angular momentum is axial vector, it is directed `bot^(ar)` to the plane of motion. | |
| 498. |
The kinetic energy of a body rotating at 300 revolutions per minute is 62.8 J. Its angular momentum (in `kg m^(2)s^(-2)`) is approximatelyA. 1B. 2C. 4D. 8 |
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Answer» Correct Answer - C 300 rpm = 5 rps `omega = 2pi (5) = 10 pi rad s^(-1)` Kinetic energy `=(1)/(2)I omega^(2)=(1)/(2)L omega` `therefore " " L = (2(KE))/(omega)=(2(62.8))/(10pi)` `= 4 kgm^(2)//s^(1)`. |
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| 499. |
The value of angular momentum of the earth rotating about its own axis isA. `7xx10^(33) kg m^(2)//s`B. `7xx10^(33) kg m^(2)//s`C. `0.7xx10^(33) kg m^(2)//s`D. zero |
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Answer» Correct Answer - A `L=I omega` `= (2)/(5) mR^(2)xx(2pi)/(T)` `=(2)/(5)xx(6xx10^(24)xx6.4xx6.4xx10^(12)xx6.28)/(86400)` `=7xx10^(33)kg m^(2)//s`. |
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| 500. |
Write the dimensional formula of angular momentum. Is it scale or vector ?A. `[L^(2)M^(1)T^(-1)]`B. `[L^(1)M^(1)T^(-1)]`C. `[L^(1)M^(1)T^(-2)]`D. `[L^(1)M^(2)T^(-1)]` |
| Answer» Correct Answer - A | |