Previous Years Problems on System of Particles and Rotional Motion for NEET

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P-8 JPME Topicwise Soved Paper- PHYSCS Previous Years Probems on Sstem of Partices and otiona Motion for NEET This Chapter Previous Years Probems on Sstem of Partices and

Topic-wise Soved Papers with 5 Mock Tests consists of past ears (memor based) soved papers from 008 onwards ti date, distributed in 9,, 8, and topics in Phsics, Chemistr,

1 P-8 JPME Topicwise Soved Paper- PHYSCS Previous Years Probems on Sstem of Partices and otiona Motion for NEET This Chapter Previous Years Probems on Sstem of Partices and otiona Motion for NEET is taken from our Book: SBN : Product Name : ear JPME Topic-wise Soved Papers (0-00) with 5 Mock Tests Product Description : ears JPME Topic-wise Soved Papers with 5 Mock Tests consists of past ears (memor based) soved papers from 008 onwards ti date, distributed in 9,, 8, and topics in Phsics, Chemistr, Bioog, Engish Language and Comprehension and Logica and Quantitative easoning respective. The book contains 000 past MCQs. The book aso contains 5 fu soved Mock Test on the atest pattern.

2 Sstem of Partices and otationa Motion P-9 Sstem of Partices and otationa Motion. The ratio of the radii of gration of a circuar disc about a tangentia axis in the pane of the disc and of a circuar ring of the same radius about a tangentia axis in the pane of the ring is [0] : (b) : (c) : (d) 5 : 6. Two bodies have their moments of inertia and respective about their axis of rotation. f their kinetic energies of rotation are equa, their anguar momenta wi be in the ratio [0] : (b) : (c) : (d) :. A uniform thin rod of weight W is supported horizonta b two vertica props at its ends. At t 0, one of these supports is kicked out. The force on the other support immediate there after is [06] W (b) W (c) W (d) W. Two objects A and B of weight 0 kg and 0 kg respective are kept at two points on the x-axis. B is moved 9 cm aong the x-axis. B what distance A shoud be moved to keep the centre of mass the same? [06] cm (b) 8 cm (c) 5 cm (d) cm 5. A sphere of radius r is roing without siding. What is the ratio of rotationa K.E. and tota K.E. associated with the sphere? [06] (b) (c) (d) 5 6. A tube of ength L is fied compete with an incompressibe iquid of mass M and cosed at both the ends. The tube is then rotated in a horizonta pane about one of its ends with a uniform anguar veocit w. The force exerted b the iquid at the other end is [06] M L/ (b) M L (c) M L/ (d) M L /. The cinders P and Q are of equa mass and ength but made of metas with densities P and Q ( P > Q ). f their moment of inertia about an axis passing through centre and norma to the circuar face be P and Q, then [06] P Q (b) P > Q (c) P < Q (d) P Q 8. A whee whose moment of inertia is kg m has an initia anguar veocit of 50 rad s. A constant torque of 0 N m acts on the whee. The time in which the whee is acceerated to 80 rad s is [05] s (b) s (c) 6 s (d) 9 s 9. Partices of masses m, m, m,..., nm grams are paced on the same ine at distances,,,..., n cm from a fixed point. The distance of centre of mass of the partices from the fixed point in centimetres is [05] (n) (b) n n( n ) (c) (d) nn ( ) 0. From a circuar disc of radius and mass 9M, a sma disc of mass M and radius is removed concentrica. The moment of inertia of the remaining disc about an axis perpendicuar to the pane of the disc and passing through its centre is [05] 0 9 (b) (c) (d) 9. The diameter of a fwhee is increased b % ncrease in its moment of inertia about the centra axis is [05] % (b) 0.5% (c) % (d) %

3 P-0 JPME Topicwise Soved Paper- PHYSCS. A chid is standing with foded hands at the centre of a patform rotating about its centra axis. The kinetic energ of the sstem is K. The chid now stretches his arms so that the moment of inertia of the sstem doubed. The kinetic energ of the sstem now is [0] K K K (b) (c) (d) K. A soid sphere of mass M and radius rotates about an axis passing through its centre making 600 rpm. ts kinetic energ of rotation is [0] (b) 5 5 (c) 80 (d) 80. Moment is inertia of a unifrom rod of enght L and mass M, about an axis passing through L/ form one end and perpendicuar to its ength is 6 ML (b) 8 ML [0] (c) 8 ML ML (d) 5. A fwhee rotates with a uniform anguar acceeration. ts anguar veocit increases from 0 rad s to 0 rad s in 0 seconds. How man rotations did it make in this period? [0] 80 (b) 00 (c) 0 (d) A kg mass is rotating on a circuar path of radius 0.8 m with anguar veocit of rad s. f radius of path becomes m, then what wi be the vaue of anguar veocit? [0] 9.8 rad s (b) 8.6 rad s (c) 8. rad s (d) 5.6 rad s. A uniform thin bar of mass 6m and ength L is bent to make a reguar hexagon. ts moment of inertia about an axis passing through the centre of mass and perpendicuar to the pane of hexagon is [0] 0mL (b) 0mL (c) 5 ml (d) 6mL 8. Two rings of radii and n made up of same materia have the ratio of moment of inertia about an axis passing through centre is : 8. The vaue of n is [0] (b) (c) (d) 9. A soid sphere and a hoow sphere of the same materia and of same size can be distinguished without weighing [0] b determining their moments of inertia about their coaxia axes (b) b roing them simutaneous on an incined pane (c) b rotating them about a common axis of rotation (d) b apping equa torque on them 0. Point masses,, and kg are ing at the points (0, 0, 0), (, 0, 0), (0,, 0) and (,, 0) respective. The moment of inertia of this sstem about X-axis wi be [0] kg m (b) kg m (c) kg m (d) kg m. The radius of gration of a bod about an axis at a distance 6 cm from its centre of mass is 0 cm. Then, its radius of gration about a parae axis through its centre of mass wi be [0] 80 cm (b) 8 cm (c) 0.8 cm(d) 80 m. A sma disc of radius cm is cut from a disc of radius 6 cm. f the distance between their centres is. cm, what is the shift in the centre of mass of the disc? [00] 0. cm (b). cm (c).8 cm (d). cm. The moment of inertia of a circuar disc of mass M and radius about an axis passing through the centre of mass is 0. The moment of inertia of another circuar disc of same mass and thickness but haf the densit about the same axis is [009] (b) (c) 8 0 (d) 0. Whan a ceiing fan is switched on, it makes 0 revoutions in the first seconds. Assuming a uniform anguar acceeration, how man rotations it wi make in the next seconds? [009] 0 (b) 0 (c) 0 (d) 0 5. A ba of radius cm and mass 8 kg ros from rest down a ramp of ength m. The ramp in incined at 5 to the horizonta. When the ba reaches the bottom, its veocit is (Take, sin and cos 5 0.8) [008] m s (b) 5 m s (c) m s (d) 6 m s 6. A drum of radius and mass M, ros down without sipping aong an incined pane of ange. The frictiona force. [00] (b) (c) (d) decreases the rotationa and transationa motion. dissipates energ as heat. decreases the rotationa motion. converts transationa energ to rotationa energ.

4 Sstem of Partices and otationa Motion P- Soutions. (d) Circuar disc...() x cm 5. (b) We know, KE rotationa 5 Circuar ring...() MK, MK K K : K 5 : 6 K. (d) K L L K L K L K K L K K L : L :. (d). (b) To keep centre of mass at same point r CM (before) r CM (Fina) m r mr m( rx) m( r 9) mm mm m r + m r m r + m x + m r + 9m m x 9m x 9m m [negecting negative sing] and KE tota 5 M CM CM K CM KE 5 rotationa KEtota Mv 5 CM KErotationa KEtota 6. The centre of mass is at L distance from the axis. L Hence, centripeta force F C M So, the reaction at the other end wi be equa to F C.. (c) Mass of cinder M i.e P Q P Q P P Q Q P P P < Q ( P > Q )...(i) (from eqn (i))

5 P- JPME Topicwise Soved Paper- PHYSCS 8. (c) nitia anguar veocit 50 rad s Fina anguar veocit 80 rad s, Torque 0 N m Moment of inertia kg m Anguar acceeration is given b 9. X CM 0 5 rad s Hence if t is the time, 5t t 6 s mx mx... mm... m m m.... mm m... m 9... m... n( n)(n) 6 (n) nn ( ) 0. Mass of the disc 9M Mass of removed portion of disc M O / The moment of inertia of the compete disc about an axis passing through its centre 0 and 9 perpendicuar to its pane is Now, the moment of inertia of the disc with removed portion M 8 Therefore, moment of inertia of the remaining portion of disc about O is (c) As we know, Taking og on both sides og og M + og Differentiating, we get d 0 + d d d % %. (b) From the aw of conservation of anguar momentum, constant As is doubed, becomes haf. K.E. of rotation, K is doubed and is haved, therefore K.E. wi become haf i.e. K.. (c) Kinetic energ of rotation ( ) (b) Moment of inertia of a uniform rod of ength L and mass M about an axis passing through the centre and perpendicuar to its ength is given b ML 0...(i) Apping the theorem of parae axes, moment of inertia of a uniform rod of ength L and mass M about an axis passing through L/ from one end and perpendicuar to its ength is given b L 0 + M ML ML ML (Using (i)) 5. (d) As we know, + t or rad s From, (0) (0) 00 or 00 No. of rotations competed (b) Given: Mass (m) kg nitia radius of the path (r ) 0.8 m nitia anguar veocit ( ) rad s Fina radius of the path (r ) m nitia moment of inertia,

6 Sstem of Partices and otationa Motion P- mr (0.8).8 kg m Fina moment of inertia mr () kg m From the aw of conservation of anguar momentum, we get rad s. Length of each side of hexagon L and mass of each side m. O 60 r L Let O be centre of mass of hexagon. Therfore perpendicuar distance of O from each side, r Ltan60 L. The desired moment of inertia of hexagon about O is m( L) 6[ one side ] 6 mr ml 6 ml ( ) 8. The moment of inertia of circuar ring whose axis of rotation is passing througth its centre is m m and m (n) Since, both have same densit m m ( n) A A where A is cross-section area of ring. m nm m m m( n) mn( n) n (Given) 8 8 or n n 9. (b) Acceeration of soid sphere is more than that of hoow sphere, it ros faster, and reaches the bottom of the incined pane earier. Hence, soid sphere and hoow sphere can be distinguished b roing them simutaneous on an incined pane. 0. Moment of inertia of the whoe sstem about the axis of rotation wi be equa to the sum of the moments of inertia of a the partices. (,, 0) kg (0,, 0) kg Y (0, 0, 9) kg (, 0, 0) kg kg m. (b) From the theorem of parae axes, the moment of inertia CM + Ma where CM is moment of inertia about centre of mass and a is the distance of axis from centre. mk m(k ) + m(6) ( mk where k is radius of gration) or, k (k ) + 6 or, 00 (k ) + 6 (k ) 6 cm k 8 cm. The situation can be shown as : Let radius of compete disc is a and that of sma disc is b. Aso et centre of mass now shifts to O at a distance x from origina centre. O a O x x b O x-axis The position of new centre of mass is given b X CM. b.x. a. b X

7 P- JPME Topicwise Soved Paper- PHYSCS Here, a 6 cm, b cm, x. cm Hence, X CM (). (6) ().8 0. cm.. (d) For circuar disc mass M, radius moment of inertia 0 For circuar disc, of same thickness t, mass M, densit then t tm As we know, moment of inertia (adius) 0 0. (c) n first three seconds, ange rotated 0 rad Using, 0 t + t (i) For the rotation of fan in next three second, the tota time of revoutions + 6 s Let tota number of revoutions N Then ange of revoutions, ' N rad N (ii) Dividing (ii) b (i), we get N 0 No. of revoution in ast three secons revoutions 5. (c) Kinetic energ K K m m mr 5 m m m ( 5 0 r) According to conservation of energ, we get 0 mv mgh 0 0 gh g sin sin 5 m s 6. (d) When a drum ros without sipping, force of friction provides the torque necessar for roing. Therefore, the frictiona force converts transationa energ to rotationa energ. h

PHYSICS LOCUS / / d dt. ( vi) mass, m moment of inertia, I. ( ix) linear momentum, p Angular momentum, l p mv l I

PHYSICS LOCUS / / d dt. ( vi) mass, m moment of inertia, I. ( ix) linear momentum, p Angular momentum, l p mv l I 6 n terms of moment of inertia, equation (7.8) can be written as The vector form of the above equation is...(7.9 a)...(7.9 b) The anguar acceeration produced is aong the direction of appied externa torque.