Rotational Mechanics PYQs Set 10 (PDF)

Set 10 of 12 · Questions 271-300 of 343

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Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 10 (Q271-300)
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271. $A mass m moves in a circle on a smooth horizontal plane with velocity v_{0} at a radius R_{0} . The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally m moves in a circle of radius \frac{R _{0}}{2} . The final value of the kinetic energy is$ (1) $2 m v_{0}^{2}$ (2) $\frac{1}{2} m v_{0}^{2}$ (3) $m v_{0}^{2}$ (4) $\frac{1}{4} m v_{0}^{2}$ 272. $To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ the torque, applied by the machine on the mop is:$ (1) $μ FR /3$ (2) $μ FR /6$ (3) $μ FR /2$ (4) $\frac{2}{3} μ FR$ 273. $Three identical uniform thin metal rods form the three sides of an equilateral triangle. If the moment of inertia of the system of these three rods about an axis passing through the centroid of the triangle and perpendicular to the plane of the triangle is n times. The moment of inertia of one rod separately about an axis passing through the centre of the rod and perpendicular to its length, the value of n is$ (1) $3$ (2) $6$ (3) $9$ (4) $12$ 274. $A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30^{\circ} . The center of mass of cylinder has speed of 4 m / s . The distance travelled by the cylinder on the inclined surface will be (Take, g = 10 m / s^{2}) [NEET 2019]$ (1) $2.2 m$ (2) $1.6 m$ (3) $1.2 m$ (4) $2.4 m$ 275. $A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :$ (1) $8.75 \times 1 0^{-4} J$ (2) $8.75 \times 1 0^{-3} J$ (3) $1.13 \times 1 0^{-3} J$ (4) $6.25 \times 1 0^{-4} J$ 276. $Consider a body shown in the figure, consisting of two identical balls, each of connected by a light rigid rod. If an impulse) = Mv (v = linear velocity of imparted to the body at one of its ends, what would be its angular velocity?$ (1) $v /4 L$ (2) $2 v / L$ (3) $v / L$ (4) $v /3 L$ 277. $For the adjoining diagram, the correct relation between I_{1}, I_{2}, and I_{3} is, (I ‐moment of inertia)$ (1) $I_{1} > I_{2}$ (2) $I_{2} > I_{1}$ (3) $I_{3} > I_{1}$ (4) $I_{3} > I_{2} .$ 278. $Four identical uniform solid spheres each of same mass ' M' and radius ' R' are placed touching each other as shown in figure, with centres A, B, C, D, I_{A}, I_{B}, I_{C} and I_{D} are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in I_{A} and I_{B} is$ (1) $24 M R^{2}$ (2) $32 M R^{2}$ (3) $56 M R^{2}$ (4) $80 M R^{2}$ 279. $A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :$ (1) $6 m$ (2) $5 m$ (3) $1 m$ (4) $2 m$ 280. $A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency ω . The ratio of v and ω is :$ (1) $66$ (2) $33$ (3) $32$ (4) $288$ 281. $The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through$ (1) $B$ (2) $C$ (3) $D$ (4) $A$ 282. $A uniform rod AB of length l and mass m is free to rotate about point A . The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is m l^{2} /3, the initial angular acceleration of the rod will be$ (1) $\frac{mgl}{2}$ (2) $\frac{3}{2} gl$ (3) $\frac{3 g}{2 l}$ (4) $\frac{2 g}{3 l} .$ 283. $Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ‘m’ and has another weight of mass 2 m hung at a distance of 75 cm from A. The tension in the string at A is:$ (1) $0.5 mg$ (2) $2 mg$ (3) $0.75 mg$ (4) $1 mg$ 284. $A rod AB of length 1 m is placed at the edge of a smooth table as shown. It is hit horizontally at point B . If the displacement of centre of mass in 1 s is 52 m, then the angular velocity of the rod is (Take, g = 10 ms^{- 2})$ (1) $30 rads^{- 1}$ (2) $20 rads^{- 1}$ (3) $10 rads^{- 1}$ (4) $5 rads^{- 1}$ 285. $In a rectangle A BC D (BC = 2 AB) . The moment of inertia is minimum along axis through$ (1) $BC$ (2) $BD$ (3) $HF$ (4) $EG$ 286. $From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?$ (1) $11 M R^{2} /32$ (2) $9 M R^{2} /32$ (3) $15 M R^{2} /32$ (4) $13 M R^{2} /32$ 287. $A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is____. (g acceleration due to gravity)$ (1) $mg /4$ (2) $mg /2$ (3) $mg /3$ (4) $mg$ 288. $The kinetic energy of a circular disc rotating with a speed of 60 r.p.m. about an axis passing through a point on its circumference and perpendicular to its plane is (mass of circular disc = 5 kg, radius of disc = 1 m) approximately.$ (1) $170 J$ (2) $160 J$ (3) $150 J$ (4) $140 J$ 289. $A thin uniform rectangular plate of mass 2 kg is placed in x - y plane as shown in figure. The moment of inertia about x -axis is I_{x} = 0.2 kg m^{2} and moment of inertia about y -axis is I_{y} = 0.3 kg m^{2} . The radius of gyration of the plate about the axis passing through O and perpendicular to the plane of the plate is$ (1) $38.7 cm$ (2) $31.6 cm$ (3) $50 cm$ (4) $5 cm$ 290. $A mass ' M' is moving with constant velocity parallel to X -axis. Its angular momentum with respect to the origin is$ (1) $constant$ (2) $decreasing$ (3) $zero$ (4) $increasing$ 291. $A thin wire of length l having a linear density ρ is bent into a circular loop with C as its centre as shown in the figure. The moment of inertia of the loop about the line AB is$ (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) $\frac{3}{8} \frac{ρ l ^{3}}{π ^{2}}$ 292. $A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights h_{sph} and h_{cyl} on the incline. The ratio \frac{h _{sph}}{h _{cyl}} is given by :$ (1) $\frac{2}{5}$ (2) $1$ (3) $\frac{14}{15}$ (4) $\frac{4}{5}$ 293. $A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder, if the rope is pulled with a force of 30 N? [NEET 2017]$ (1) $25 m / s^{2}$ (2) $0.25 rad / s^{2}$ (3) $25 rad / s^{2}$ (4) $5 m / s^{2}$ 294. $Five solid spheres each of mass ' m' and radius ' r' are rotating about an axis A A^{’} as shown in figure. Hence the moment of inertia of the system about the axis of rotation A A^{’} is$ (1) $5 mr^{2}$ (2) $4 m r^{2}$ (3) $3 m r^{2}$ (4) $6 m r^{2}$ 295. $A solid sphere is projected up along an inclined plane of inclination 30^{\circ} with the horizontal with a speed of 4 ms^{- 1} . If it rolls without slipping, the maximum distance traversed by it is (g = 10 ms^{- 2})$ (1) $2.24 m$ (2) $112 m$ (3) $1.12 m$ (4) $22.4 m$ 296. $A solid cylinder of mass 2 kg and radius 4 cm rotating about its axis at the rate of 3 rpm. The torque required to stop after 2π revolutions is:$ (1) $2 \times 1 0^{6} Nm$ (2) $2 \times 1 0^{-6} Nm$ (3) $2 \times 1 0^{-3} Nm$ (4) $12 \times 1 0^{-4} Nm$ 297. $From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the center? [NEET 2016]$ (1) $13 M R^{2} /32$ (2) $11 M R^{2} /32$ (3) $9 M R^{2} /32$ (4) $15 M R^{2} /32$ 298. $A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30º from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s^{-1}) will be (g = 10 m/ s^{-2})$ (1) (2) (3) (4) 299. $A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from A to B, the angular momentum of the particle about ' O'$ (1) $remains constant$ (2) $increases$ (3) $first increases then decreases$ (4) $decreases.$ 300. $A uniform circular disc of radius ' R' and mass ' M' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R /2 is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.$ (1) $\frac{7}{32} MR^{2}$ (2) $\frac{9}{32} MR^{2}$ (3) $\frac{17}{32} MR^{2}$ (4) $\frac{13}{32} MR^{2}$