Rotational Mechanics PYQs Set 12 (PDF)

Set 12 of 14 · Questions 331-360 of 410

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Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 12 (Q331-360)
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331. $The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through$ (1) $B$ (2) $C$ (3) $D$ (4) $A$ 332. $A uniform rod AB of length l and mass m is free to rotate about point A . The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is m l^{2} /3, the initial angular acceleration of the rod will be$ (1) $\frac{mgl}{2}$ (2) $\frac{3}{2} gl$ (3) $\frac{3 g}{2 l}$ (4) $\frac{2 g}{3 l} .$ 333. $Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ‘m’ and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is:$ (1) $0.5 mg$ (2) $2 mg$ (3) $0.75 mg$ (4) $1 mg$ 334. $A rod AB of length 1 m is placed at the edge of a smooth table as shown. It is hit horizontally at point B . If the displacement of centre of mass in 1 s is 52 m, then the angular velocity of the rod is (Take, g = 10 ms^{- 2})$ (1) $30 rads^{- 1}$ (2) $20 rads^{- 1}$ (3) $10 rads^{- 1}$ (4) $5 rads^{- 1}$ 335. $In a rectangle A BC D (BC = 2 AB) . The moment of inertia is minimum along axis through$ (1) $BC$ (2) $BD$ (3) $HF$ (4) $EG$ 336. $From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?$ (1) $11 M R^{2} /32$ (2) $9 M R^{2} /32$ (3) $15 M R^{2} /32$ (4) $13 M R^{2} /32$ 337. $A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is____. (g acceleration due to gravity)$ (1) $mg /4$ (2) $mg /2$ (3) $mg /3$ (4) $mg$ 338. $The kinetic energy of a circular disc rotating with a speed of 60 r.p.m. about an axis passing through a point on its circumference and perpendicular to its plane is (mass of circular disc = 5 kg, radius of disc = 1 m) approximately.$ (1) $170 J$ (2) $160 J$ (3) $150 J$ (4) $140 J$ 339. $A thin uniform rectangular plate of mass 2 kg is placed in x - y plane as shown in figure. The moment of inertia about x -axis is I_{x} = 0.2 kg m^{2} and moment of inertia about y -axis is I_{y} = 0.3 kg m^{2} . The radius of gyration of the plate about the axis passing through O and perpendicular to the plane of the plate is$ (1) $38.7 cm$ (2) $31.6 cm$ (3) $50 cm$ (4) $5 cm$ 340. $A mass ' M' is moving with constant velocity parallel to X -axis. Its angular momentum with respect to the origin is$ (1) $constant$ (2) $decreasing$ (3) $zero$ (4) $increasing$ 341. $A thin wire of length l having a linear density ρ is bent into a circular loop with C as its centre as shown in the figure. The moment of inertia of the loop about the line AB is$ (1) $\frac{5}{16} \frac{ρ l ^{3}}{π ^{3}}$ (2) $\frac{1}{16} \frac{ρ l ^{3}}{π ^{3}}$ (3) $\frac{1}{8} \frac{ρ l ^{3}}{π ^{3}}$ (4) $\frac{3}{8} \frac{ρ l ^{3}}{π ^{2}}$ 342. $A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights h_{sph} and h_{cyl} on the incline. The ratio \frac{h _{sph}}{h _{cyl}} is given by :$ (1) $\frac{2}{5}$ (2) $1$ (3) $\frac{14}{15}$ (4) $\frac{4}{5}$ 343. $A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder, if the rope is pulled with a force of 30 N? [NEET 2017]$ (1) $25 m / s^{2}$ (2) $0.25 rad / s^{2}$ (3) $25 rad / s^{2}$ (4) $5 m / s^{2}$ 344. $Five solid spheres each of mass ' m' and radius ' r' are rotating about an axis A A^{’} as shown in figure. Hence the moment of inertia of the system about the axis of rotation A A^{’} is$ (1) $5 mr^{2}$ (2) $4 m r^{2}$ (3) $3 m r^{2}$ (4) $6 m r^{2}$ 345. $A solid sphere is projected up along an inclined plane of inclination 30^{\circ} with the horizontal with a speed of 4 ms^{- 1} . If it rolls without slipping, the maximum distance traversed by it is (g = 10 ms^{- 2})$ (1) $2.24 m$ (2) $112 m$ (3) $1.12 m$ (4) $22.4 m$ 346. $A solid cylinder of mass 2 kg and radius 4 cm rotating about its axis at the rate of 3 rpm. The torque required to stop after 2π revolutions is:$ (1) $2 \times 1 0^{6} Nm$ (2) $2 \times 1 0^{-6} Nm$ (3) $2 \times 1 0^{-3} Nm$ (4) $12 \times 1 0^{-4} Nm$ 347. $From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the center? [NEET 2016]$ (1) $13 M R^{2} /32$ (2) $11 M R^{2} /32$ (3) $9 M R^{2} /32$ (4) $15 M R^{2} /32$ 348. $A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30º from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s^{-1}) will be (g = 10 m/ s^{-2})$ (1) (2) (3) (4) 349. $A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from A to B, the angular momentum of the particle about ' O'$ (1) $remains constant$ (2) $increases$ (3) $first increases then decreases$ (4) $decreases.$ 350. $A uniform circular disc of radius ' R' and mass ' M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R /2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.$ (1) $\frac{7}{32} MR^{2}$ (2) $\frac{9}{32} MR^{2}$ (3) $\frac{17}{32} MR^{2}$ (4) $\frac{13}{32} MR^{2}$ 351. $A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:$ (1) $Mg 1 - (\frac{R - a}{R})^{2}$ (2) $Mg (\frac{R}{R - a})^{2} - 1$ (3) $Mg 1 - \frac{a ^{2}}{R ^{2}}$ (4) $Mg \frac{a}{R}$ 352. $An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is :(Take g = 10 m/ s^{2})$ (1) $240N$ (2) $90N$ (3) $300N$ (4) $30N$ 353. $A particle of mass m is moving along a trajectory given by x = x_{0} + a cos ω_{1} t y = y_{0} + b sin ω_{2} t The torque, acting on the particle about the origin, at t = 0 is:$ (1) $m (- x_{0} b + y_{0} a) ω_{1}^{2} k^$ (2) $+ m y_{0} a ω_{1}^{2} k^$ (3) $Zero$ (4) $- m (x_{0} b ω_{2}^{2} - y_{0} a ω_{1}^{2}) k^$ 354. $A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity ω . Its kinetic energy is$ (1) $\frac{1}{2} m r^{2} ω^{2}$ (2) $mr ω^{2}$ (3) $m r^{2} ω^{2}$ (4) $\frac{1}{4} m r ω^{2}$ 355. $A fly wheel rotating about fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is$ (1) $0.6 kg m^{2}$ (2) $0.15 kg m^{2}$ (3) $0.8 kg m^{2}$ (4) $0.75 kg m^{2}$ 356. $A gramophone record is revolving with an angular velocity ω . A coin is placed at a distance r from the centre of the record. The static coefficient of friction is μ . The coin will revolve with the record if$ (1) $r = μg ω^{2}$ (2) $r < \frac{ω ^{2}}{μg}$ (3) $r \leq \frac{μg}{ω ^{2}}$ (4) $r \geq \frac{μg}{ω ^{2}}$ 357. $Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω_{1} and ω_{2} . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is$ (1) $\frac{1}{4} I (ω_{1} - ω_{2})^{2}$ (2) $I (ω_{1} - ω_{2})^{2}$ (3) $\frac{1}{8} I (ω_{1} - ω_{2})^{2}$ (4) $\frac{1}{2} I (ω_{1} + ω_{2})^{2}$ 358. $A person of 80kg mass is standing on the rim of a circular platform of mass 200kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre ________.$ 359. $Three balls of masses 2 kg, 4 kg and 6 kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 m . The moment of intertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ____kgm^{2} .$ 360. $A circular disc of mass M and radius R is rotating about its axis with angular speed ω_{1} . If another stationary disc having radius \frac{R}{2} and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω_{2} . The energy lost in the process is p% of the initial energy. Value of p is:$