Rotational Mechanics PYQs Set 8 (PDF)

Set 8 of 14 · Questions 211-240 of 410

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Mere Teacher · Previous Year Questions JEE Main Physics · Rotational Mechanics · Set 8 (Q211-240)
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211. $Three identical uniform solid spheres each of mass m and radius r are joined as shown in the figure, with centres lying in the same plane. The moment of inertia of the system about an axis lying in that plane and passing through the centre of sphere C is$ (1) $\frac{16}{5} m r^{2}$ (2) $\frac{12}{5} m r^{2}$ (3) $4 m r^{2}$ (4) $\frac{3}{5} m r^{2}$ 212. $A solid spherical ball rolls on a horizontal surface at 10 m / s and continues to roll up on an inclined surface as shown in the figure. If the mass of the ball is 11 kg and frictional losses are negligible, the value of h where the ball stop and starts rolling down the inclination is (Assume, g = 10 m / s^{2})$ (1) $8 m$ (2) $6 m$ (3) $7 m$ (4) $10 m$ 213. $A thin circular plate of mass M and radius R has its density varying as ρ (r) = ρ_{0} r with ρ_{0} as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I = a MR^{2} . The value of the coefficient a is:$ (1) $½$ (2) $3/5$ (3) $8/5$ (4) $\frac{3}{2}$ 214. $A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is$ (1) $\frac{F}{3 m R}$ (2) $\frac{F}{2 m R}$ (3) $\frac{3 F}{2 m R}$ (4) $\frac{2 F}{3 m R}$ 215. $A square Lamina OABC of length 10 cm is pivoted at ' O '. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is:$ (1) $10N$ (2) $0(zero)$ (3) $10 \sqrt 2 N$ (4) $20N$ 216. $A particle of mass 20 g is released with an initial velocity \frac{5 m}{s} along the curve from the point A, as shown in the figure. The point A is at height h from point B . The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be : (Take (g = \frac{10 m}{s ^{2}})$ (1) $2 kg - \frac{m ^{2}}{s}$ (2) $8 kg - m ^{2}$ (3) $6 kg - m^{2} / s$ (4) $3 kg - m^{2} / s$ 217. $A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is : [The coefficient of static friction, μ_{s}, is 0.4]$ (1) $\frac{7}{2} mg$ (2) $5 mg$ (3) $\frac{mg}{5}$ (4) $0$ 218. $Three point-masses m_{1}, m_{2} and m_{3} are located at the vertices of an equilateral triangle, having each side of length L . The moment of inertia of the system about an axis along an altitude of the triangle passing through m_{1} is given by$ (1) $I = (m_{1} + m_{2} + m_{3}) L^{2}$ (2) $I = (m_{1} + m_{2}) \frac{L ^{2}}{2}$ (3) $I = (m_{2} + m_{3}) L^{2}$ (4) $I = (m_{2} + m_{3}) \frac{L ^{2}}{4}$ 219. $As shown in the figure, a bob a mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius R and mass m . When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be:$ (1) $\frac{1}{R} \frac{4 gh}{3}$ (2) $\frac{1}{R} \frac{2 gh}{3}$ (3) $R \frac{2 gh}{3}$ (4) $R \frac{4 gh}{3}$ 220. $A slab is subjected to two forces F_{1} and F_{2} of same magnitude F as shown in the figure. Force F_{2} is in XY - plane while force F_{1} acts along z - axis at the point (2 i + 3 j) The moment of these forces about point O will be:$ (1) $(3 i - 2 j + 3 k) F$ (2) $(3 i - 2 j - 3 k) F$ (3) $(3 i + 2 j - 3 k) F$ (4) $(3 i + 2 j + 3 k) F$ 221. $A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?$ (1) $Both reach at the same time$ (2) $Depends on their masses$ (3) $Disc$ (4) $Sphere$ 222. $A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R(R = radius of the earth), it ejects a rocket of mass \frac{m}{10} that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :$ (1) $5 M (u^{2} - \frac{119 GM}{200 R})$ (2) $5 M (u^{2} - \frac{113 GM}{200 R})$ (3) $\frac{M}{20} (u^{2} - \frac{119 GM}{200 R})$ (4) $\frac{M}{20} (u^{2} - \frac{113 GM}{200 R})$ 223. $A disc of radius R and mass M is rolling horizontally without slipping with speed v . It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :$ (1) $\frac{v ^{2}}{g}$ (2) $\frac{3}{4} \frac{v ^{2}}{g}$ (3) $\frac{1}{2} \frac{v ^{2}}{g}$ (4) $\frac{2}{3} \frac{v ^{2}}{g}$ 224. $Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. Themoment of inertia of the system about an axis passing through A and parallel to DB would be :$ (1) $m /2$ (2) $2 ml^{2}$ (3) $3 ml^{2}$ (4) $3 m l^{2}$ 225. $Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be 1. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:$ (1) $12 cm$ (2) $16 cm$ (3) $14 cm$ (4) $18 cm$ 226. $A particle of mass 5 m at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular direction with speed v each. The energy released during the process is$ (1) $\frac{3}{5} m v^{2}$ (2) $\frac{5}{3} m v^{2}$ (3) $\frac{3}{2} m v^{2}$ (4) $\frac{4}{3} m v^{2}$ 227. $A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t_{1} and t_{2}, respectively, then$ (1) $t_{1} > t_{2}$ (2) $t_{1} = t_{2}$ (3) $t_{1} < t_{2}$ (4) $t_{1} = 2 t_{2}$ 228. $The radius of gyration of a uniform rod of length L, about an axis passing through a point \frac{L}{4} away from the centre of the rod, and perpendicular to it, is:$ (1) $\frac{7}{48} L$ (2) $\frac{5}{48} L$ (3) $\frac{7}{24} L$ (4) $\frac{19}{24} L$ 229. $Two particles A, B are moving on two concentric circles of radii R_{1} and R_{2} with equal angular speed ω . At t = 0, their positions and direction of motion are shown in the figure : The relative velocity v_{A}^{\to} - v_{B} and t = \frac{π}{2 ω} is given by:$ (1) $ω (R_{1} + R_{2}) i$ (2) $- ω (R_{1} + R_{2}) i$ (3) $ω (R_{2} - R_{1}) i$ (4) $ω (R_{1} - R_{2}) i$ 230. $A thin uniform rod of mass ' m' and length ' l ' is suspended from one end which can oscillate in a vertical plane about the point of intersection. It is pulled to one side and then released. It passes through the equllibrium position with angular sped 'o.' "We kinetle energy while passing through mean position is$ (1) $m l^{2} w^{2}$ (2) $\frac{m l ^{2} ω ^{2}}{4}$ (3) $\frac{m l ^{2} ω ^{2}}{6}$ (4) $\frac{m l ^{2} ω ^{2}}{12}$ 231. $Point masses m_{1} and m_{2} are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ω_{0} is minimum, is given by$ (1) $x = \frac{m _{2}}{m _{1}} L$ (2) $x = \frac{m _{2} L}{m _{1} + m _{2}}$ (3) $x = \frac{m _{1} L}{m _{1} + m _{2}}$ (4) $x = \frac{m _{1}}{m _{2}} L$ 232. $A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle θ The frictional force$ (1) $dissipates energy as heat$ (2) $decreases the rotational motion$ (3) $decreases the rotational and translational motion$ (4) $converts translational energy to rotational energy.$ 233. $A light rod of length l has two masses m_{1} and m_{2} attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the center of mass is [NEET 2016]$ (1) $\frac{m _{1} m _{2}}{m _{1} + m _{2}} l^{2}$ (2) $\frac{m _{1} + m _{2}}{m _{1} m _{2}} l^{2}$ (3) $(m_{1} + m_{2}) l^{2}$ (4) $m_{1} m_{2} l^{2}$ 234. $Three rods each of mass 1 kg and length 2 m are joined together end-to-end to form an equilateral triangle ABC . Find the moment of inertia of this system about an axis passing through its centre of mass and perpendicular to the plane of the triangle.$ (1) $4 kg - m^{2}$ (2) $2 kg - m^{2}$ (3) $3 kg - m^{2}$ (4) $6 kg - m^{2}$ 235. $Four particles each of mass 1 kg are placed at four corners of a square of side 2 m . Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is______kgm^{2} .$ 236. $Two iron solid discs of negligible thickness have radii R_{1} and R_{2} and moment of intertia I_{1} and I_{2}, respectively. For R_{2} = 2 R_{1}, the ratio of I_{1} and I_{2} would be 1/ x, where x = -$ 237. $A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of 2 rad / s^{2} . Moment of intertia of the wheel is ________kg m^{2} . (Acceleration due to gravity = 10 m / s^{2})$ 238. $Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is______x 1 0^{- 3} kg m^{2} .$ 239. $If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be \frac{x}{7} . The value of x is_______.$ 240. $A force of - P k^acts on the origin of the coordinate system. The torque about the point (2, -3) is P (a i^+ b j^), The ratio of \frac{a}{b} is \frac{x}{2} . The value of x is$