Rotational Mechanics PYQs Set 11 (PDF)

Set 11 of 14 · Questions 301-330 of 410

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Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 11 (Q301-330)
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301. $A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with a angular speed ω rad/s about the vertical. About the point of suspension :$ (1) $angular momentum is conserved.$ (2) $angular momentum changes in magnitude but not in direction$ (3) $angular momentum changes in direction but not in magnitude.$ (4) $angular momentum changes both in direction and magnitude.$ 302. $A cord is wound round the circumference of wheel of radius r . The axis of the wheel is horizontal and themoment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. Afterfalling through a distance ’ h ’, the square of angular velocity of wheel will be:$ (1) $2 gh I+mr2$ (2) $2 gh$ (3) $\frac{2 mgh}{I + 2 m r ^{2}}$ (4) $\frac{2 mgh}{I + m r ^{2}}$ 303. $A triangular plate is shown. A force F = 4 i - 3 j is applied at point P . The torque at point P with respect to point ’ O^{’} and ’ Q ’ are :$ (1) $- 15 - 203, 15 - 203$ (2) $15 + 203, 15 - 203$ (3) $15 - 203, 15 + 203$ (4) $- 15 + 203, 15 + 203$ 304. $An object of mass ' m ' is projected from origin in a vertical xy plane at an angle 45^{\circ} with the x axis with an initial velocity v_{0} . The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [g is acceleration due to gravity]$ (1) $\frac{m v _{o}^{3}}{2 2 g} along negative z-axis$ (2) $\frac{m v _{o}^{3}}{4 2 g} along positive z-axis$ (3) $\frac{m v _{o}^{3}}{4 2 g} along negative z-axis$ (4) $\frac{m v _{o}^{3}}{2 2 g} along positive z-axis$ 305. $A rigid massless rod of length 3 l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:$ (1) $\frac{g}{13 l}$ (2) $\frac{g}{3 l}$ (3) $\frac{g}{2 l}$ (4) $\frac{7 g}{3 l}$ 306. $The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB(Which is ⊥to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)$ (1) $R^{2} : r^{2}$ (2) $2 r^{2} : R^{2}$ (3) $2 R^{2} : r^{2}$ (4) $2 R^{4} : r^{4}$ 307. $A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is :$ (1) (2) (3) (4) 308. $Four point masses, each of mass m, are fixed at the corners of a square of side l . The square is rotating with angular frequency ω, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is :$ (1) $3 m l^{2} ω$ (2) $4 m l^{2} ω$ (3) $m l^{2} ω$ (4) $2 m l^{2} ω$ 309. $Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :$ (1) $\frac{73}{2} M R^{2}$ (2) $\frac{181}{2} M R^{2}$ (3) $\frac{19}{2} M R^{2}$ (4) $\frac{55}{2} M R^{2}$ 310. $A sphere of radius ’ a ’ and mass 'm' rolls along horizontal plane with constant speed u_{-} 0 . It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping how far up the sphere willtravel?$ (1) $\frac{2}{5} \frac{v _{0}^{2}}{g sin θ}$ (2) $\frac{10 v _{0}^{2}}{7 g sin θ}$ (3) $\frac{v _{0}^{2}}{5 g sin θ}$ (4) $\frac{v _{0}^{2}}{2 g sin θ}$ 311. $A rod PQ of mass M and length L is hinged at end P . The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is$ (1) $\frac{2 g}{L}$ (2) $\frac{2 g}{2 L}$ (3) $\frac{3 g}{2 L}$ (4) $\frac{g}{L}$ 312. $A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 9 0^{o} . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is$ (1) $\frac{M L ^{2}}{6}$ (2) $\frac{2 M L ^{2}}{24}$ (3) $\frac{M L ^{2}}{24}$ (4) $\frac{M L ^{2}}{12}$ 313. $A circular disc D_{1} of mass M and radius R has two identical D_{2} and D_{3} of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertiaof the system about the axis OO', passing through the centre of D_{1}, as shown in the figure, will be :$ (1) $MR^{2}$ (2) $3 MR^{2}$ (3) $45 MR^{2}$ (4) $\frac{2}{3} M R^{2}$ 314. $A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string):$ (1) $20 rad/ s^{2}$ (2) $16 rad/ s^{2}$ (3) $10 rad/ s^{2}$ (4) $12 rad/ s^{2}$ 315. $A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity σ). If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity$ (1) $\frac{ωM}{M + 2 m}$ (2) $\frac{ω ( M + 2 m )}{M}$ (3) $\frac{ωM}{M + m}$ (4) $\frac{ω ( M - 2 m )}{M + 2 m}$ 316. $A mass m moves in a circle on a smooth horizontal plane with velocity v_{0} at a radius R_{0} . The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally m moves in a circle of radius \frac{R _{0}}{2} . The final value of the kinetic energy is$ (1) $2 m v_{0}^{2}$ (2) $\frac{1}{2} m v_{0}^{2}$ (3) $m v_{0}^{2}$ (4) $\frac{1}{4} m v_{0}^{2}$ 317. $To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ the torque, applied by the machine on the mop is:$ (1) $μ FR /3$ (2) $μ FR /6$ (3) $μ FR /2$ (4) $\frac{2}{3} μ FR$ 318. $Three identical uniform thin metal rods form the three sides of an equilateral triangle. If the moment of inertia of the system of these three rods about an axis passing through the centroid of the triangle and perpendicular to the plane of the triangle is n times. The moment of inertia of one rod separately about an axis passing through the centre of the rod and perpendicular to its length, the value of n is$ (1) $3$ (2) $6$ (3) $9$ (4) $12$ 319. $A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30^{\circ} . The center of mass of cylinder has speed of 4 m / s . The distance travelled by the cylinder on the inclined surface will be (Take, g = 10 m / s^{2}) [NEET 2019]$ (1) $2.2 m$ (2) $1.6 m$ (3) $1.2 m$ (4) $2.4 m$ 320. $A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :$ (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) $6.25 \times 1 0^{-4} J$ 321. $Consider a body shown in the figure, consisting of two identical balls, each of connected by a light rigid rod. If an impulse) = Mv (v = linear velocity of imparted to the body at one of its ends, what would be its angular velocity?$ (1) $v /4 L$ (2) $2 v / L$ (3) $v / L$ (4) $v /3 L$ 322. $For the adjoining diagram, the correct relation between I_{1}, I_{2}, and I_{3} is, (I ‐moment of inertia)$ (1) $I_{1} > I_{2}$ (2) $I_{2} > I_{1}$ (3) $I_{3} > I_{1}$ (4) $I_{3} > I_{2} .$ 323. $Four identical uniform solid spheres each of same mass ' M' and radius ' R' are placed touching each other as shown in figure, with centres A, B, C, D, I_{A}, I_{B}, I_{C} and I_{D} are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in I_{A} and I_{B} is$ (1) $24 M R^{2}$ (2) $32 M R^{2}$ (3) $56 M R^{2}$ (4) $80 M R^{2}$ 324. $A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :$ (1) $6 m$ (2) $5 m$ (3) $1 m$ (4) $2 m$ 325. $A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency ω . The ratio of v and ω is :$ (1) $66$ (2) $33$ (3) $32$ (4) $288$ 326. $A 2kg steel rod of length 0.6m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity, Ignoring the friction due to clamping at its lower end, the speed of the free end of rod when it passes through its lowest position is ... m s^{- 1} ... (Take g = 10 m s^{- 2})$ 327. $An massless equilateral triangle EFG of side ' a ’ (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG inthe plane of EFG is \frac{N}{20} m a^{2} where N is an integer. The value of N is ___________.$ 328. $A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m/s at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s. After 2s it acquires a purely rolling motion (see figure), The total kinetic energy of the disc after 2s will be________J (given, coefficient of friction is 0.3 and g=10m/ s^{2}).$ 329. $The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, n = ______ Consider all the bodies have equal masses.$ 330. $Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is \frac{x}{12} ML^{2} kg m^{2} . The value of x is____.$