Rotational Mechanics PYQs Set 9 (PDF)

Set 9 of 12 · Questions 241-270 of 343

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions NEET Physics · Rotational Mechanics · Set 9 (Q241-270)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
241. $A particle of mass m = 5 is moving with a uniform speed v = 32 in the XOY plane along the line Y = X + 4 . The magnitude of the angular momentum of the particle about the origin is$ (1) $60 units$ (2) $402 units$ (3) $zero$ (4) $7.5 units$ 242. $A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as (\frac{σ _{0}}{r}), then the radius of gyration of the disc about its axis passing through the centre is :$ (1) $\frac{a ^{2} + b ^{2} + ab}{2}$ (2) $\frac{a + b}{2}$ (3) $\frac{a ^{2} + b ^{2} + ab}{3}$ (4) $\frac{a + b}{3}$ 243. $From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about at perpendicular axis, passing through the centre ?$ (1) $9 M R^{2} /32$ (2) $15 M R^{2} /32$ (3) $13 M R^{2} /32$ (4) $11 M R^{2} /32$ 244. $Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d . The ratio \frac{I _{0}}{I _{A}} of moment of inertial h of the system about an axis passing the centroid and about center of any of the spheres I_{A} and perpendicular to the plane of the triangle is :$ (1) $13/23$ (2) $11/19$ (3) $7/9$ (4) $13/11$ 245. $When a mass is rotating in a plane about a fixed point, its angular momentum is directed along$ (1) $a line perpendicular to the plane of rotation$ (2) $the lin2 making an angle of45o to the plane of rotation$ (3) $the radius$ (4) $the tangent to the orbit$ 246. $A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in figure. The point A is at height h from point B. The particle sides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be :$ (1) $3 kg- m^{2} /s$ (2) $6 kg- m^{2} /s$ (3) $2 kg- m^{2} /s$ (4) $8 kg- m^{2} /s$ 247. $Shown in the figure is a hollow ice-cream cone (it open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is:$ (1) $\frac{M ( R ^{2} + H ^{2} )}{4}$ (2) $\frac{M R ^{2}}{2}$ (3) $\frac{M R ^{2}}{3}$ (4) $\frac{M H ^{2}}{3}$ 248. $A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5 s, is close to:$ (1) $4.0 \times 10^{- 6} Nm$ (2) $1.6 \times 10^{- 5} Nm$ (3) $7.9 \times 10^{- 6} Nm$ (4) $2.0 \times 10^{- 5} Nm$ 249. $Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is 8/ x . The value of x is :$ (1) $51$ (2) $34$ (3) $17$ (4) $67$ 250. $Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ (r) = A + Br . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is :$ (1) $2 π a^{4} (\frac{A}{4} + \frac{Ba}{5})$ (2) $2 π a^{4} (\frac{Aa}{4} + \frac{B}{5})$ (3) $π a^{4} (\frac{A}{4} + \frac{Ba}{5})$ (4) $2 π a^{4} (\frac{A}{5} + \frac{Ba}{4})$ 251. $A rod of length L revolves in a horizontal plane about the axis passing through its centre and perpendicular to its length. The angular velocity of the rod is ω . If A is the area of cross-section of the rod and ρ is its density, then the rotational kinetic energy of the rod is$ (1) $\frac{1}{3} A L^{3} ρ ω^{2}$ (2) $\frac{1}{2} A L^{3} ρ ω^{2}$ (3) $\frac{1}{24} A L^{3} ρ ω^{2}$ (4) $\frac{1}{18} A L^{3} ρ ω^{2}$ 252. $A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30^{\circ} from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rads^{- 1}) will be (g = 10 ms^{- 2})$ (1) $\frac{30}{7}$ (2) $30$ (3) $\frac{20}{3}$ (4) $\frac{30}{2}$ 253. $Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about$ (1) $\frac{16}{5} m r^{2}$ (2) $4 m r^{2}$ (3) $\frac{11}{5} m r^{2}$ (4) $3 m r^{2}$ 254. $A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45^{\circ} at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms^{- 2})$ (1) $200 N$ (2) $140 N$ (3) $70 N$ (4) $100 N$ 255. $A solid spherical ball is rolled up an inclined plane of angle of inclination 30^{\circ} with an initial speed of 4 m / s at the bottom of the inclination. How far will the ball go up the plane. (Use g = 10 m / s^{2})$ (1) $56 cm$ (2) $112 cm$ (3) $224 cm$ (4) $120 cm$ 256. $A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with a angular speed ω rad/s about the vertical. About the point of suspension :$ (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) $angular momentum changes both in direction and magnitude.$ 257. $A cord is wound round the circumference of wheel of radius r . The axis of the wheel is horizontal and themoment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. Afterfalling through a distance ’ h ’, the square of angular velocity of wheel will be:$ (1) $2 gh I+mr2$ (2) $2 gh$ (3) $\frac{2 mgh}{I + 2 m r ^{2}}$ (4) $\frac{2 mgh}{I + m r ^{2}}$ 258. $A triangular plate is shown. A force F = 4 i - 3 j is applied at point P . The torque at point P with respect to point ’ O^{’} and ’ Q ’ are :$ (1) $- 15 - 203, 15 - 203$ (2) $15 + 203, 15 - 203$ (3) $15 - 203, 15 + 203$ (4) $- 15 + 203, 15 + 203$ 259. $An object of mass ' m ' is projected from origin in a vertical xy plane at an angle 45^{\circ} with the x axis with an initial velocity v_{0} . The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [g is acceleration due to gravity]$ (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) $\frac{m v _{o}^{3}}{2 2 g} along positive z-axis$ 260. $A rigid massless rod of length 3 l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:$ (1) $\frac{g}{13 l}$ (2) $\frac{g}{3 l}$ (3) $\frac{g}{2 l}$ (4) $\frac{7 g}{3 l}$ 261. $The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB(Which is ⊥to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)$ (1) $R^{2} : r^{2}$ (2) $2 r^{2} : R^{2}$ (3) $2 R^{2} : r^{2}$ (4) $2 R^{4} : r^{4}$ 262. $A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is :$ (1) (2) (3) (4) 263. $Four point masses, each of mass m, are fixed at the corners of a square of side l . The square is rotating with angular frequency ω, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about this axis is :$ (1) $3 m l^{2} ω$ (2) $4 m l^{2} ω$ (3) $m l^{2} ω$ (4) $2 m l^{2} ω$ 264. $Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :$ (1) $\frac{73}{2} M R^{2}$ (2) $\frac{181}{2} M R^{2}$ (3) $\frac{19}{2} M R^{2}$ (4) $\frac{55}{2} M R^{2}$ 265. $A sphere of radius ’ a ’ and mass 'm' rolls along horizontal plane with constant speed u_{-} 0 . It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping how far up the sphere willtravel?$ (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) $\frac{v _{0}^{2}}{2 g sin θ}$ 266. $A rod PQ of mass M and length L is hinged at end P . The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is$ (1) $\frac{2 g}{L}$ (2) $\frac{2 g}{2 L}$ (3) $\frac{3 g}{2 L}$ (4) $\frac{g}{L}$ 267. $A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 9 0^{o} . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is$ (1) $\frac{M L ^{2}}{6}$ (2) $\frac{2 M L ^{2}}{24}$ (3) $\frac{M L ^{2}}{24}$ (4) $\frac{M L ^{2}}{12}$ 268. $A circular disc D_{1} of mass M and radius R has two identical D_{2} and D_{3} of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertiaof the system about the axis OO', passing through the centre of D_{1}, as shown in the figure, will be :$ (1) $MR^{2}$ (2) $3 MR^{2}$ (3) $45 MR^{2}$ (4) $\frac{2}{3} M R^{2}$ 269. $A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string):$ (1) $20 rad/ s^{2}$ (2) $16 rad/ s^{2}$ (3) $10 rad/ s^{2}$ (4) $12 rad/ s^{2}$ 270. $A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity σ). If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity$ (1) $\frac{ωM}{M + 2 m}$ (2) $\frac{ω ( M + 2 m )}{M}$ (3) $\frac{ωM}{M + m}$ (4) $\frac{ω ( M - 2 m )}{M + 2 m}$