Rotational Mechanics PYQs Set 14 (PDF)

Set 14 of 14 · Questions 391-410 of 410

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

Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 14 (Q391-410)
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.
391. $Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:$ (1) $14 cm$ (2) $16 cm$ (3) $18 cm$ (4) $12 cm$ 392. $A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s-2$ (1) $25 N$ (2) $50 N$ (3) $78.5 N$ (4) $157 N$ 393. $A particle of mass m = 5 units is moving with uniform speed v = 32 units in the XY -plane along the line Y = X + 4 . The magnitude of the angular momentum about origin is$ (1) $zero$ (2) $60 units$ (3) $7.5 units$ (4) $40 units$ 394. $A mass 'm' supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release$ (1) $\frac{2 g}{3}$ (2) $\frac{g}{2}$ (3) $\frac{5 g}{6}$ (4) $g$ 395. $A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is :$ (1) $g/L$ (2) $2g/L$ (3) $\frac{2 g}{3 L}$ (4) $\frac{3 g}{2 L}$ 396. $Angular momentum of a single particle moving with constant speed along circular path :$ (1) $changes in magnitude but remains same in the direction$ (2) $remains same in magnitude and direction$ (3) $remains same in magnitude but changes in the direction$ (4) $is zero$ 397. $A uniform rod of length ‘ l ’ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To find θ equate the rate of change of angular momentum (direction going into the paper) \frac{m l ^{2}}{12} ω^{2} sin θ cos θ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces F_{H} and F_{v}, about the CM. The value of θ is then such that :$ (1) $cos θ = \frac{g}{l ω ^{2}}$ (2) $cos θ = \frac{g}{3 l ω ^{2}}$ (3) $cos θ = \frac{g}{2 l ω ^{2}}$ (4) $cos θ = \frac{3 g}{2 l ω ^{2}}$ 398. $From a uniform circular disc of radius R and mass 9 M, a small disc of radius \frac{R}{3} is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is :$ (1) $10 M R^{2}$ (2) $\frac{37}{9} M R^{2}$ (3) $4 M R^{2}$ (4) $\frac{40}{9} M R^{2}$ 399. $A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be:$ (1) $\frac{5}{3}$ (2) $\frac{4}{5}$ (3) $\frac{3}{5}$ (4) $\frac{14}{15}$ 400. $A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_{t}) as well as rotational kinetic energy (K_{r}) simultaneously. The ratio K_{t} : (K_{t} + R_{r}) for the sphere is :$ (1) $7 : 10$ (2) $2 : 5$ (3) $10 : 7$ (4) $5 : 7$ 401. $ABC is an equilateral triangle with O as its centre. F_{1}, F_{2} an d F_{3} represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero the magnitude of F_{3} is :$ (1) $F1 + F2$ (2) $F1 - F2$ (3) $\frac{F _{1} + F _{2}}{2}$ (4) $2 (F1 + F2)$ 402. $A rectangular solid box of length 0.3 m is held horizontally with one of its sides on the edge of a platform of height 5 m When released, it slips off the table in a very short time τ = 0.01 s s, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (ir radians) close to :$ (1) $0.5$ (2) $0.3$ (3) $0.02$ (4) $0.28$ 403. $A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :$ (1) $7.5 rad$ (2) $15 rad ‘$ (3) $20 rad$ (4) $30 rad$ 404. $Moment of inertia of a disc of mass M and radius 'R' about any of its diameter is \frac{M R ^{2}}{4} . The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, \frac{x}{2} M R^{2} . The value of x is_____.$ 405. $The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I_{1} . The same rod is bent into a ring and its moment of inertia about a diameter is I_{2} . If \frac{I _{1}}{I _{2}} is \frac{x π ^{2}}{3}, then the value of x will be_______.$ 406. $A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is t (1 - e^{- π /2}) . The value of t is$ 407. $Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio of \frac{x}{6} . The value of x is$ 408. $I_{C M} is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. I_{A B} is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance \frac{2}{3} R from center. Where R is the radius of the disc. The ratio of I_{A B} and I_{C M} is x: 9. The value of x is___.$ 409. $A uniform solid cylinder with radius R and length L has moment of inertia I_{1}, about the axis of cylinder. A concentric solid cylinder of radius R' = \frac{R}{2} and length L' = \frac{L}{2} is caned out of the original cylinder. If I_{2} is the moment of inertia of the carved out portion to the cylinder then \frac{I _{1}}{I _{2}} = ________(Both I_{1} and I_{2} are about the axis of the cylinder)$ 410. $Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \frac{r}{2} distance from the end A of the handle will be \dots. M r^{2}$