Rotational Mechanics PYQs Set 8 (PDF)

Set 8 of 12 · Questions 211-240 of 343

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Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 8 (Q211-240)
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211. $A circular disc D_{1} of mass M and radius R has two identical discs D_{2} and D_{3} of the same mass M and radius R attached rigidly at its opposite ends (see figure.) The moment of inertia of the system about the axis OO', passing through the centre of D_{v} as shown in the figure, will be:$ (1) $\frac{2}{3} M R^{2}$ (2) $M R^{2}$ (3) $3 M R^{2}$ (4) $\frac{4}{5} M R^{2}$ 212. $Consider a disc of radius R and mass M . A hole of radius \frac{R}{3} is created in the disk such that the center of the hole is \frac{R}{3} away from centre of the disk. The moment of inertia of the system along the axis perpendicular to the disc passing through the centre of the disc is$ (1) $\frac{MR ^{2}}{2}$ (2) $\frac{13}{27} MR^{2}$ (3) $\frac{1}{3} MR^{2}$ (4) $4 MR^{2}$ 213. $Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2 R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:$ (1) $\frac{137}{15} MR^{2}$ (2) $\frac{17}{15} MR^{2}$ (3) $\frac{209}{15} MR^{2}$ (4) $\frac{152}{15} MR^{2}$ 214. $A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes halfofrotation (Ifradius of wheel is 1 m)$ (1) $2 m$ (2) $π^{2} + 4 m$ (3) $πm$ (4) $π^{2} + 2 m .$ 215. $An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m s^{- 1} to keep it in position. The number of bullets fired per second by the machine gun is :$ (1) $50$ (2) $25$ (3) $100$ (4) $5$ 216. $Solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is :-$ (1) $\frac{2}{5}$ (2) $\frac{2}{7}$ (3) $\frac{1}{5}$ (4) $\frac{7}{10}$ 217. $Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is 43 \times 10^{5} dyne. cm , the angular acceleration of the discs about the given axis AB is____rad / s^{2} .$ (1) $11$ (2) $22$ (3) $100$ (4) $27$ 218. $The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is$ (1) $M R^{2}$ (2) $\frac{1}{2} M R^{2}$ (3) $\frac{3}{2} M R^{2}$ (4) $\frac{7}{2} M R^{2}$ 219. $A particle of mass m is projected with a speed u from the ground at an angle θ = π/3 w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity u i^. The horizontal distance covered by the combined mass before reaching the ground is :$ (1) $\frac{3 3}{8} \frac{u ^{2}}{g}$ (2) $22 \frac{u ^{2}}{g}$ (3) $\frac{5}{8} \frac{u ^{2}}{g}$ (4) $\frac{3 2}{4} \frac{u ^{2}}{g}$ 220. $A small object of uniform density rolls up a curved surface with an initial velocity ‘v’. It reaches upto a maximum height of \frac{3 v ^{2}}{4 g} with respect to the initial position. The object is$ (1) $hollow sphere$ (2) $disc$ (3) $ring$ (4) $solid sphere$ 221. $A solid cylinder has mass ' M', radius ' R' and length ' t . Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is$ (1) $\frac{2 M R ^{2}}{3} + \frac{M l ^{2}}{12}$ (2) $\frac{M R ^{2}}{3} + \frac{M l ^{2}}{12}$ (3) $\frac{3 M R ^{2}}{4} + \frac{M l ^{2}}{12}$ (4) $\frac{M R ^{2}}{4} + \frac{M l ^{2}}{12}$ 222. $A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass m is suspended from the rod at 160 cm mark as shown in the figure. Find the value of m such that the rod is in equilibrium. (g = 10 m / s^{2}) [NEET 2021]$ (1) $\frac{1}{2} kg$ (2) $\frac{1}{3} kg$ (3) $\frac{1}{6} kg$ (4) $\frac{1}{12} kg$ 223. $A particle of mass m moves in the XY plane with a velocity v along the straight line AB . If the angular momentum of the particle with respect to origin O is L_{A} when it is at A and L_{B} when it is at B, then$ (1) $L_{A} = L_{B}$ (2) $the relationship between L_{A} and L_{B} depends upon the slope of the line AB$ (3) $L_{A} < L_{B}$ (4) $L_{A} > L_{B} .$ 224. $The moment of inertia of a thin uniform rectangular plate of mass ' m', having length 'a' and width ' b' about an axis perpendicular to the plane of the plate and passing through one of its vertices is$ (1) $\frac{2}{3} mab$ (2) $\frac{1}{3} mab$ (3) $\frac{2}{3} m (a^{2} + b^{2})$ (4) $\frac{1}{3} m (a^{2} + b^{2})$ 225. $A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is$ (1) $2.5 m / s^{2}$ (2) $3.5 m / s^{2}$ (3) $0.25 m / s^{2}$ (4) $0.35 m / s^{2}$ 226. $If force F = 3 i^+ 4 j^- 2 k^acts on a particle having position vector 2 i^+ j^+ 2 k^then, the torque about the origin will be :-$ (1) $3 i^+ 4 j^- 2 k^$ (2) $- 10 i^+ 10 j^+ 5 k^$ (3) $10 i^+ 5 j^- 10 k^$ (4) $10 i^+ j^- 5 k^$ 227. $Four identical solid spheres each of mass ’ m ’ and radius ’ a ’ are placed with their centres on the four corners of asquare of side ’ b ’ . The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :$ (1) $\frac{4}{5} m a^{2}$ (2) $\frac{8}{5} m a^{2} + m b^{2}$ (3) $\frac{4}{5} m a^{2} + 2 m b^{2}$ (4) $\frac{8}{5} m a^{2} + 2 m b^{2}$ 228. $A uniform solid cylinder of mass ' m' and radius ' r' rolls along an inclined rough plane of inclination 45^{\circ} . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be$ (1) $\frac{1}{2} g$ (2) $\frac{1}{3 2} g$ (3) $\frac{2 g}{3}$ (4) $2 g$ 229. $A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively)? [NEET 2024]$ (1) $Point P moves slower than point Q$ (2) $Point P moves faster than point Q$ (3) $Both the points P and Q move with equal speed$ (4) $Point P has zero speed$ 230. $The solid cylinder of length 80cm and mass M has a radius of 20cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7kg m^{2} .$ (1) $14.9kg/ m^{3}$ (2) $7. 5 x 1 0^{1} kg/ m^{3}$ (3) $7. 5 x 1 0^{2} kg/ m^{3}$ (4) $1. 49 x 1 0^{2} kg/ m^{3}$ 231. $Four point masses, each of mass M are placed at the corners of a square of side L . The moment of inertia of the system about one of its diagonals is$ (1) $2 M L^{2}$ (2) $M L^{2}$ (3) $4 M L^{2}$ (4) $6 M L^{2}$ 232. $ABC is an equilateral triangle with O as its centre. F_{1}, F_{2} and F_{3} represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of F_{3} is$ (1) $F_{1} + F_{2}$ (2) $F_{1} - F_{2}$ (3) $F_{1} + F_{2} 2$ (4) $2 (F_{1} + F_{2})$ 233. $Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio Ι0/ΙA of moment of inertial Ι0 of the system about an axis passing the centroid and about center of any of the spheres ΙA and perpendicular to the plane of the triangle is :$ (1) $\frac{23}{13}$ (2) $\frac{13}{15}$ (3) $\frac{13}{23}$ (4) $\frac{15}{13}$ 234. $A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/ s^{2})$ (1) $\frac{π}{6}$ (2) $\frac{π}{2}$ (3) $\frac{π}{4}$ (4) $\frac{π}{3}$ 235. $A square frame ABCD is formed by four identical rods each of mass ' m' and length ' l'. This frame is in X - Y plane such that side AB coincides with X -axis and side AD along Y -axis. The moment of inertia of the frame about X -axis is$ (1) $\frac{5 m l ^{2}}{3}$ (2) $\frac{2 m l ^{2}}{3}$ (3) $\frac{4 m l ^{2}}{3}$ (4) $\frac{m l ^{2}}{12}$ 236. $A uniform thin rod of 120 cm length and 1600 g mass is bent as shown in the figure. The moment of inertia of the bent rod about an axis passing through the point ' O' and perpendicular to the plane of the paper is\dots\dots\dots kg - m^{2} .$ (1) $0.084$ (2) $0.360$ (3) $0.018$ (4) $0.120$ 237. $A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?$ (1) $Depends on their masses$ (2) $Disk$ (3) $Sphere$ (4) $both reach at the same time$ 238. $Moment of inertia of a rod of mass ' M ' and length ' L ' about an axis passing through its center and normal to its length is ' α'. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is:$ (1) $α /4$ (2) $α /8$ (3) $α$ (4) $α /2$ 239. $Point masses m_{1} and m_{2} are placed at the opposite ends of a rigid rod of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass, so that the work required to set the rod rotating with angular velocity ω_{o} is minimum, is given by$ (1) $x = \frac{m _{1} L}{m _{1} + m _{2}}$ (2) $x = \frac{m _{1}}{m _{2}} L$ (3) $x = \frac{m _{2}}{m _{1}} L$ (4) $x = \frac{m _{2} L}{m _{1} + m _{2}}$ 240. $For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O ’ (corner point) is :$ (1) $1/2$ (2) $1/4$ (3) $1/8$ (4) $2/3$