Rotational Mechanics PYQs Set 9 (PDF)

Set 9 of 14 · Questions 241-270 of 410

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Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 9 (Q241-270)
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241. $A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, would be:$ (1) $20 rad / s$ (2) $30 rad / s$ (3) $10 rad / s$ (4) $0 rad / s$ 242. $A particle of mass ' m' is moving along a line y = x + a with a constant velocity ' v'. The angular momentum of the particle about the origin is$ (1) $mva$ (2) $mva 2$ (3) $\frac{mva}{2}$ (4) $\frac{mva}{x 2}$ 243. $It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is , while for its similar collision with carbon nucleus at rest, fractional loss of energy is . The values of and are respectively :$ (1) $(0, 0)$ (2) $(0, 1)$ (3) $(.89, .28)$ (4) $(.28, .89)$ 244. $A small object of uniform density rolls up a curved surface with an initial velocity ‘ν’ . It reaches upto a maximum height of \frac{3 ν ^{2}}{4 g} with respect to the initial position. The object is$ (1) $Solid sphere$ (2) $Hollow sphere$ (3) $Disc$ (4) $Ring$ 245. $A circular disc D_{1} of mass M and radius R has two identical discs D_{2} and D_{3} of the same mass M and radius R attached rigidly at its opposite ends (see figure.) The moment of inertia of the system about the axis OO', passing through the centre of D_{v} as shown in the figure, will be:$ (1) $\frac{2}{3} M R^{2}$ (2) $M R^{2}$ (3) $3 M R^{2}$ (4) $\frac{4}{5} M R^{2}$ 246. $Consider a disc of radius R and mass M . A hole of radius \frac{R}{3} is created in the disk such that the center of the hole is \frac{R}{3} away from centre of the disk. The moment of inertia of the system along the axis perpendicular to the disc passing through the centre of the disc is$ (1) $\frac{MR ^{2}}{2}$ (2) $\frac{13}{27} MR^{2}$ (3) $\frac{1}{3} MR^{2}$ (4) $4 MR^{2}$ 247. $Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2 R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:$ (1) $\frac{137}{15} MR^{2}$ (2) $\frac{17}{15} MR^{2}$ (3) $\frac{209}{15} MR^{2}$ (4) $\frac{152}{15} MR^{2}$ 248. $A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes halfofrotation (Ifradius of wheel is 1 m)$ (1) $2 m$ (2) $π^{2} + 4 m$ (3) $πm$ (4) $π^{2} + 2 m .$ 249. $An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m s^{- 1} to keep it in position. The number of bullets fired per second by the machine gun is :$ (1) $50$ (2) $25$ (3) $100$ (4) $5$ 250. $Solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is :-$ (1) $\frac{2}{5}$ (2) $\frac{2}{7}$ (3) $\frac{1}{5}$ (4) $\frac{7}{10}$ 251. $Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is 43 \times 10^{5} dyne. cm , the angular acceleration of the discs about the given axis AB is____rad / s^{2} .$ (1) $11$ (2) $22$ (3) $100$ (4) $27$ 252. $The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is$ (1) $M R^{2}$ (2) $\frac{1}{2} M R^{2}$ (3) $\frac{3}{2} M R^{2}$ (4) $\frac{7}{2} M R^{2}$ 253. $A particle of mass m is projected with a speed u from the ground at an angle θ = π/3 w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity u i^. The horizontal distance covered by the combined mass before reaching the ground is :$ (1) $\frac{3 3}{8} \frac{u ^{2}}{g}$ (2) $22 \frac{u ^{2}}{g}$ (3) $\frac{5}{8} \frac{u ^{2}}{g}$ (4) $\frac{3 2}{4} \frac{u ^{2}}{g}$ 254. $A small object of uniform density rolls up a curved surface with an initial velocity ‘v’. It reaches upto a maximum height of \frac{3 v ^{2}}{4 g} with respect to the initial position. The object is$ (1) $hollow sphere$ (2) $disc$ (3) $ring$ (4) $solid sphere$ 255. $A solid cylinder has mass ' M', radius ' R' and length ' t . Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is$ (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) $\frac{M R ^{2}}{4} + \frac{M l ^{2}}{12}$ 256. $A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass m is suspended from the rod at 160 cm mark as shown in the figure. Find the value of m such that the rod is in equilibrium. (g = 10 m / s^{2}) [NEET 2021]$ (1) $\frac{1}{2} kg$ (2) $\frac{1}{3} kg$ (3) $\frac{1}{6} kg$ (4) $\frac{1}{12} kg$ 257. $A particle of mass m moves in the XY plane with a velocity v along the straight line AB . If the angular momentum of the particle with respect to origin O is L_{A} when it is at A and L_{B} when it is at B, then$ (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) $L_{A} > L_{B} .$ 258. $The moment of inertia of a thin uniform rectangular plate of mass ' m', having length 'a' and width ' b' about an axis perpendicular to the plane of the plate and passing through one of its vertices is$ (1) $\frac{2}{3} mab$ (2) $\frac{1}{3} mab$ (3) $\frac{2}{3} m (a^{2} + b^{2})$ (4) $\frac{1}{3} m (a^{2} + b^{2})$ 259. $A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is$ (1) $2.5 m / s^{2}$ (2) $3.5 m / s^{2}$ (3) $0.25 m / s^{2}$ (4) $0.35 m / s^{2}$ 260. $If force F = 3 i^+ 4 j^- 2 k^acts on a particle having position vector 2 i^+ j^+ 2 k^then, the torque about the origin will be :-$ (1) $3 i^+ 4 j^- 2 k^$ (2) $- 10 i^+ 10 j^+ 5 k^$ (3) $10 i^+ 5 j^- 10 k^$ (4) $10 i^+ j^- 5 k^$ 261. $Four identical solid spheres each of mass ’ m ’ and radius ’ a ’ are placed with their centres on the four corners of asquare of side ’ b ’ . The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :$ (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) $\frac{8}{5} m a^{2} + 2 m b^{2}$ 262. $A uniform solid cylinder of mass ' m' and radius ' r' rolls along an inclined rough plane of inclination 45^{\circ} . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be$ (1) $\frac{1}{2} g$ (2) $\frac{1}{3 2} g$ (3) $\frac{2 g}{3}$ (4) $2 g$ 263. $A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively)? [NEET 2024]$ (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) $Point P has zero speed$ 264. $The solid cylinder of length 80cm and mass M has a radius of 20cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2.7kg m^{2} .$ (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) $1. 49 x 1 0^{2} kg/ m^{3}$ 265. $Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by \frac{x}{256} M r^{2} . The value of x is____.$ 266. $A circular plate is rotating in horizontal plane, about an axis passing through its centre and perpendicular to the plate, with an angular velocity ω . A person sits at the centre having two dumbbells in his hands. When he stretched out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be \frac{E}{x} . The value of x is$ 267. $ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I_{0} . If part ADE is removed, the moment of inertia of the remaining part about the same axis is \frac{N l _{0}}{16} where N is an integer. Value of N is ____________.$ 268. $A thin rod of mass 0.9kg and length 1m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1kg moving in a straight line with velocity 80m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rodimmediately after the collision will be$ 269. $A pulley of radius 1.5 m is rotated about its axis by a force F = (12t - 3 t^{2}) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4.5 kg m^{2}, the number of rotations made by the pulley before its direction of motion is reversed, will be \frac{K}{π} . The value of K is____.$ 270. $A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is________N. (Take g = 10 m s^{- 2})$