Rotational Mechanics PYQs Set 12 (PDF)

Set 12 of 12 · Questions 331-343 of 343

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Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 12 (Q331-343)
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331. $Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:$ (1) $14 cm$ (2) $16 cm$ (3) $18 cm$ (4) $12 cm$ 332. $A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s-2$ (1) $25 N$ (2) $50 N$ (3) $78.5 N$ (4) $157 N$ 333. $A particle of mass m = 5 units is moving with uniform speed v = 32 units in the XY -plane along the line Y = X + 4 . The magnitude of the angular momentum about origin is$ (1) $zero$ (2) $60 units$ (3) $7.5 units$ (4) $40 units$ 334. $A mass 'm' supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release$ (1) $\frac{2 g}{3}$ (2) $\frac{g}{2}$ (3) $\frac{5 g}{6}$ (4) $g$ 335. $A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is :$ (1) $g/L$ (2) $2g/L$ (3) $\frac{2 g}{3 L}$ (4) $\frac{3 g}{2 L}$ 336. $Angular momentum of a single particle moving with constant speed along circular path :$ (1) $changes in magnitude but remains same in the direction$ (2) $remains same in magnitude and direction$ (3) $remains same in magnitude but changes in the direction$ (4) $is zero$ 337. $A uniform rod of length ‘ l ’ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To find θ equate the rate of change of angular momentum (direction going into the paper) \frac{m l ^{2}}{12} ω^{2} sin θ cos θ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces F_{H} and F_{v}, about the CM. The value of θ is then such that :$ (1) $cos θ = \frac{g}{l ω ^{2}}$ (2) $cos θ = \frac{g}{3 l ω ^{2}}$ (3) $cos θ = \frac{g}{2 l ω ^{2}}$ (4) $cos θ = \frac{3 g}{2 l ω ^{2}}$ 338. $From a uniform circular disc of radius R and mass 9 M, a small disc of radius \frac{R}{3} is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is :$ (1) $10 M R^{2}$ (2) $\frac{37}{9} M R^{2}$ (3) $4 M R^{2}$ (4) $\frac{40}{9} M R^{2}$ 339. $A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be:$ (1) $\frac{5}{3}$ (2) $\frac{4}{5}$ (3) $\frac{3}{5}$ (4) $\frac{14}{15}$ 340. $A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_{t}) as well as rotational kinetic energy (K_{r}) simultaneously. The ratio K_{t} : (K_{t} + R_{r}) for the sphere is :$ (1) $7 : 10$ (2) $2 : 5$ (3) $10 : 7$ (4) $5 : 7$ 341. $ABC is an equilateral triangle with O as its centre. F_{1}, F_{2} an d F_{3} represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero the magnitude of F_{3} is :$ (1) $F1 + F2$ (2) $F1 - F2$ (3) $\frac{F _{1} + F _{2}}{2}$ (4) $2 (F1 + F2)$ 342. $A rectangular solid box of length 0.3 m is held horizontally with one of its sides on the edge of a platform of height 5 m When released, it slips off the table in a very short time τ = 0.01 s s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (ir radians) close to :$ (1) $0.5$ (2) $0.3$ (3) $0.02$ (4) $0.28$ 343. $A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :$ (1) $7.5 rad$ (2) $15 rad ‘$ (3) $20 rad$ (4) $30 rad$