rotational motion qns

7/27/2019 Rotational Motion Qns

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QUEST TUTORIALSHead Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439

Q221. A shell fired from a gun at an angle to the horizontal explodes in mid air. The centre of mass of the shell fragments will

have

(a) vertically down

(b) horizontally

(c) along the same parabolic path of the unexploded shell

(d) along the tangent to the parabolic path of unexploded shell

Q222. The centre of mass of a system of two particles is

(a) on the line joining then and midway between them

(b) on the line joining them at a point whose distance from each particle is proportional to the square of the mass f theparticle

(c) on the line joining them and at a point whose distance from each particle is proportional inversely to the mass of

that particle

(d) on the line joining them and at a point whose distance from each particle is proportional to the mass of that particle

Q223. Of the two spheres of same size, mass and appearance one is hollow and other is solid. If the two are rolled down an

inclined plane simultaneously, then

(a) hollow sphere will reach the bottom first

(b) solid sphere will reach the bottom first

(c) both will reach bottom together

(d) either can reach first depending upon the surface of the plane

Q224. A loaded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation . The gun is initially

at rest on a horizontal frictionless surface. After firing, the centre of mass of the gunshot system

(a) moves with a velocity vm/M

(b) moves wit a velocity vm/M cosin the horizontal direction(c) remains at rest

(d) moves with a velocity( )

( )mM

mMv

in the horizontal direction

Q225. If a mass of mass M jumps to the ground from a height h and his centre of mass moves a distance x in the time taken by

him to hit the ground, the average force acting on him (assuming constant retardation) is

(a) Mgh/x (b) Mgx/h (c) Mg(h/x)2 (d) Mg(x/h)

2

Q226. The motion of the centre of mass of a system of two particles is unaffected by their interval forces

(a) only if these are along the line joining the particles

(b) only if there are at right angles to the line joining the particles(c) only if there are obliquely inclined to the line joining the particle

(d) irrespective of the actual direction of the interval forces

Q227. The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis is

(a) 1 : 2 (b) 5 : 6 (c) 2 : 3 (d) 2 : 1

Q228. A massive circular hoop of radius r oscillates in its own plane about a horizontal axis at a distance x above the centre of

the hoop. The period of oscillation is minimum, when x equals

(a) r (b) r/2 (c) r/3 (d) zero

Q229. A jet engine works on the principle of conservation of

(a) mass (b) energy (c) linear momentum (d) Angular momentum

Q230. A rectangular container half full of petrole is being carried by a train on a horizontal track. If the train accelerates, the

surface of the petrole in the container with respect to horizontal surface will

(a) be raised upward from the front (b) be raised in the middle(c) be raised upward from the back (d) remain unchanged

Q231. A rod of length L revolves with angular velocity about an axis through its centre and perpendicular to its length. If A

is the area of crosssection of the rod and d its density, then its kinetic energy will be

(a) dA3

1 23 (b) dA2

1 23 (c) dA2

1 22 (d) dA3

1 22

Q232. A particle moves in a circle with uniform speed. When its goes from pt A to diametrically opposite point B, its

momentum changes by Aa PP

= 2 kg m/s j and the centripetal force acting on it changes by AB AF

= 8N i . The

angular velocity of the particle is


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(a) 4 radian/s (b) 16 radian/s (c) 2/rad/sec (d) dependent upon its massQ233. For the particle in the above problem (Q232), if the displacement in 1/4

thof the time period is 0.3 m, the radius of the

circle is nearly

(a) 0.11 m (b) 1.2/2 m (c) 0.15 m (d) 0.6/mQ234. A sphere and right circular cylinder have both same mass and radius. The moment of inertia (MI) of sphere about its

diameter

(a) more than MI of cylinder about its axis

(b) equal to MI of cylinder about its axis

(c) les than MI of cylinder abut its axis(d) can be more or less than MI of cylinder about its axis depending upon the length of the cylinder

Q235. If both the sphere and cylinder (question no. 234) roll down the same incline sphere will reach bottom

(a) earlier than cylinder (b) later than cylinder

(c) at the same time as cylinder (d) earlier or later depending upon the surface

Q236.

Q237.

Q238. Two identical uniform rods P and Q move

with same velocity v as shown in the figure.

The rod Q has aG additional angular velocity

(< 6v/ ) clockwise abut G

A AB B

G

v v

G

P

(a) If ends A and Aare suddenly fixed simultaneously both rods with rotate with the same angular velocity

(b) If ends A and Aare fixed simultaneously, the rod Q will rotate with greater angular velocity

(c) If the ends B and Bare suddenly fixed both rod will rotate with same angular velocity

(d) If the ends B and Bare fixed simultaneously the rod will rotate greater angular velocityQ239. A uniform circular disc placed on a rough horizontal surface has initially a linear velocity v0and an angular velocity

w0. If the disc comes to rest after moving some distance in the direction of motion, then v0/r0is(a) 1/2 (b) 1 (c) 3/2 (d) 2

Q240. A solid right circular cylinder is placed on a rough plane of inclination to the horizontal. The coefficient of frictionbetween the cylinder and the plane so that the cylinder rolls down (without sliding) is

(a) tan (b) sin (c) 1/3 tan (d) 3/2 tanQ241. A uniform rod AB of mass in length at rest on a smooth horizontal surface is subject to an impulse P at the end B.

The time taken by the rod of turn through a right angle is

(a) 2m 1/p (b) 2p/m (c) m /12 p (d) p/m

Q242. A particle moves along an arc of a circle of radius R. Its velocity depends upon the distance covered as v = aS, a

being a constant. The angle between the total acceleration vector and velocity vector is given by

(a) tan= 2 S/R (b) sin= S/R (c) sinR

S2 (d) tan= (2S/R)

Q243. A mass m on a frictionless table is attached to a hanging mass M by a chord through a hole in the tale surface. The

angular velocity with which the mass in must rotate on a circle of radius r such that mass M may hang in equilibrium at

rest is

(a)mr

Mg (b)

Mr

mg (c)

r

g

M

m1

+ (d)

r

g

Mm

Mm

+

Q244. The trajectory of a fixed point on the rain of a wheel of a vehicle as the vehicle moves with a constant speed is being

observed by an observer fixed on ground. The trajectory, as noted by him will be

(a) a circle coinciding with circumference of the wheel repeating itself

(b) a parabola with vertex at the highest point on the wheel

(c) a straight line parallel to road

(d) a cycloid, repeating itself with every rotation of the wheel

Q245. One end of a light inextensible string is fixed to a point on a smooth horizontal table. A mass 3m is tied to the other

extremity and a mass m is tied at the mid point of the string. Both the masses remain on the table with string straight and

taut. The mass are now so projected on the table that they revolve in circles with uniform sped about the fixed end of string

such that the two parts of string remains in straight line. The ratio of the tensions in the two parts of the string is given by


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(a) 1 : 2 (b) 1 : 3 (c) 3 : 2 (d) 6 : 7

Q246. A particle of mass m is placed inside a hemispherical bowl of radius 102 m. rotating about its vertical axis with

constant angular velocity . The particle is just prevented from sliding down when the radius vector OP joining it to thecentre of the bowl makes an angle of 45 with the axis. If the coefficient of friction between the particle and the bowl is

0.5, the value fo (given g = 10 ms2) is

(a) 2 rad/s (b) 1/3 rad/s (c) 3 rad/sec (d) 1/3 rad/secQ247. A wheel of mass 4M in the form of a disc of radius r is accelerated from rest about a fixed axis through the centre by a

constant tangential force of magnitude Mg for 10 sec. The angular speed of the wheel at the end of 10 sec will be

(a) g/r rad/sec (b) 5r/g rad/sec (c) 4g/r rad/sec (d) 5g/r rad/secQ248. The rotor of a helicopter has 4 blades, each of length 2m and making 10 rev/second. A tip of one of the blades

weighing 1 kg is lost in an accident. The resultant sideways force on the helicopter is approximately

(a) 100 N (b) 2000 N (c) 5000 N (d) 8000 N

Q249. Three garden rollers have the same diameter and total mass. The roller A has most of the mass concentrated on rain.

The roller B has the mass concentrated near the axle while the roller C is uniform solid cylinder. If the rollers are listed

in order according to the case with which they may be accelerated, it will be

(a) ABC (b) ACB (c) BAC (d) BCA

Q250. The moment of inertia plays the same role in rotational motion as is played in linear motion by

(a) velocity (b) momentum (c) energy (d) mass

Q251. The driving wheel of a belt drive attached to an electric motor has a diameter of 38 cm and operates at 1200 ?. The

tension in the belt is 130 N on the slack side and 600 N on the tight side. The power transmitted tote wheel by the belt is

(a) 5 kw (b) 7.5 kw (b) 10.6 kw (d) 11.2 kw

Q252. The human body can withstand an acceleration a times that due to gravity. The minimum radius of curvature with

which a plot may safely turn a plane vertically ? at the end of a dive when the planes speed is 770 km/hrs.

(a) 519 m (b) 612 m (c) 475 m (d) 323 m

Q253. At time t, a particle of mass m has position vector r = r cos i + r sinj . If the angular momentum of the particle

about the origin C k all the time, C being a constant, the value of is

(a) =mr

Ct (b) =

2mr

Ct (c) =

C

tmr2

(d) =2

2

Cr

mt

Q254. A particle moves in a circle of radius 4 cm. clockwise at constant

speed 2cm/sec. If x and y are unit accelerations vectors along x

and y respectively (in cm s2), the accelerates of the particle half

way between P & Q is given by

P

y

Qx

O

(a) 4 ( )yx+ (b) 4 ( )yx+ (c) ( ) 2/yx+ (d) ( ) 4/yx+ s

Q255. If is the angular velocity vector for earths rotation and R and V are position and velocity vectors for a particle

irrespectively in earths reference frame, then carioles acceleration is given by

(a) (R) (b) v (c) 2v (d) v Q256. A student sitting on a pivoted stool holds the axle of a bicycle vertical. Holding the stool, the wheel is set into spinning,

with angular momentum L0upwards. Now the stool is released and the student suddenly turns the axle upside down by

180. As a result the student and stool will start spinning with angular momentum(a) L0upwards (b) 2L0upwards (c) 2L0downwards (d) L0 downwards

Q257. A symmetrical wheel radius 12 cm is mounted on its axis kept horizontal. A light cord is wrapped round the wheel and

supports a 0.40 Kg mass. If this is released from rest, with the string taut, the object is observed to fall with acceleration

3ms2. Given g = 10 ms

2, the moment of inertia of wheel about its axis is nearest to (Kg m

2)

(a) 0.0135 (b) 0.0192 (c) 1.35 (d) 192

Q258. A closed tube, partly filed with a liquid and set horizontal is rotated about a vertical axis passing through its centre. In

the process the momentum of inertia of the system about its axis would

(a) increase always

(b) decrease always


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(c) remain constant

(d) increase if the tube is less than half filled, decrease otherwise

Q259. A uniform rigid rod has length L and mass m. It lies on a horizontal smooth surface and is rotated at a uniform angular

velocity about a vertical axis passing through one of its ends. The force exerted by the axle on the rod will be

(a) m2L outwards (b) m2L inwards (c) 1/2 m2L outwards (d) 1/2 m2L inwardsQ260. A wheel is rolling straight on ground without slipping.

If the axis of the wheel has speed v, the instantaneous

velocity of a point P on the rim defined by angle

relative to ground will be

P

(a) v cos (/2) (b) 2v cos (/2) (c) v (1 + sin) (d) v (1 + cos)

Q261. A uniform ring of radius r and mass per unit length P is spun about its axis with an angular velocity . The increase intension due to stretching of the ? is proportional to

(a) r22 (b) r2 (c) r2 (d) 1/2r22Q262. A wheel of radius 40 cm. rolls over a plane with angular velocity 10Hz without slipping. Which of the following

statements is true ?

(a) The speed of its centre of mass is 8 ms1

(b) The speed of its point of contact with the plane is zero

(c) The velocities at the ends of horizontal diameter are equal

(d) Velocity at the upper end of vertical diameter is 4 ms1

horizontally

Q263. A particle of mass m is executing uniform circular motion abut affixed axis with speed v. If r

and F

are radius vectorand centripetal force respectively, the value of torque is

(a) zero (b) positive non zero constant

(c) negative non zero constant (d) variable

Q264. The angular momentum for the above particle (Q 264) is

(a) zero (b) mv/r (c) mvr (d) infinity

Q265. The areal velocity for the above particle (Q 264)is

(a) zero (b) 1/2 (dr/dt)2 (c) r (d) 1/2 vr

Q266. For a particle rotating about a fixed axis with nonuniform angular velocity, there(a) is only radial acceleration

(b) is only tangential acceleration

(c) is neither radial nor tangential acceleration

(d) are both radial acceleration and tangential acceleration

Q267. A particle moves in the XY plane in a circular path with constant velocity about the z axis in clockwise direction. Forthis particle

(a) angular momentum and torque point in the same direction

(b) angular momentum and linear momentum point in the same direction

(c) angular momentum and angular velocity are in the same direction

(d) angular momentum and linear velocity are in the same direction.

Q268. A particle moves in the XY plane about the Zaxisin the anticlockwise direction with uniform velocity.

The direction of the angular velocity is along

(a) Xaxis

(b) Yaxis

(c) + Zaxis

(d) Zaxis

Z

Y

X

Q269. A rigid body rotates abut a fixed axis by the application of a force. For this body

(a) the direction of angular momentum is along the direction of torque

(b) The direction of change of angular momentum is along the direction of torque

(c) the direction of angular momentum is along the direction of force

(d) the direction of change of angular momentum is along the direction of force.

Q270. If the total external force acting on a rigid body is zero, then

(a) only linear momentum remains constant


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(b) only angular momentum remains constant

(c) both linear momentum and angular momentum remains constant

(d) neither linear momentum nor angular momentum remain constant

Q271. The moment of inertia of a plane circular disc (Mass M radius R) about an axis passing through its centre and

perpendicular to its plane is (1/2 MR2). The momentum of inertia about one of its diameters will be

(a) 1/4 MR2 (b) 1/2 MR

2 (c) MR

2 (d) 2 MR2

Q272. Three bodies of same mass are rotating about a

symmetrical axis passing through each as shown with

the same angular speed. Then

M

MM

I1 I

2

I3

(a) I1= I2= I3 (b) I1> I2> I3 (c) I1< I2< I3 (d) none of the above

Q273. A hollow cylinder and a solid cylinder both having same mass and same radius are rotating abut their axis with the

same constant angular speed. Then moment of inertia of solid cylinder

(a) will always be more than that of hollow cylinder

(b) will always be equal to that of hollow cylinder

(c) will always be less than that of hollow cylinder

(d) will be equal, less or more than that of hollow cylinder depending upon the speed of rotation

Q274. One end of a string of length is connected to a particle of mass m and the other to a small peg on a smooth horizontal

table. If the particle moves in a circle with speed v, the net force on the particle is (T tension in the string)

(a) T directed towards the centre (b) T e

mv2directed towards centre

(c) T +e

mv2

directed away from centre (d) zero

Q275. A stone of mass m is tied to a string of length is whirled round in a horizontal plane in a circle of radius r. The speed

of the stone is increased beyond the maximum permissible value and the string breaks suddenly; then

(a) the stone will jerk radially outwards

(b) the stone will jerk radially inwards

(c) the stone will fly off tangentially from the instant the string breaks

(d) the stone flies off at an angle , such that tanis proportional to the speed of the stoneQ276. Which of the following statements is false

(a) During rolling the force of friction acts in the same direction as the direction of motion of the centre of mass of the

body

(b) The instantaneous speed of the point of contact during rolling is zero

(c) The instantaneous acceleration of the point of contact during rolling is zero

(d) For perfect rolling, work done against friction is zero

Q277. The moment of inertia of a thin uniform rod of mass M and length about an axis passing through its centre and

perpendicular to its length is ML2/12. The momentum of inertia about a parallel axes through its end is

(a) M 2/12 (b) M

2/6 (c) M

2/3 (d) M

2/2

Q278. Which of the statements about the momentum of inertia of a body is true

(a) Moment of inertia of a body is always constant independent of the axis about which it rotate(b) Moment of inertia of a body depends upon the speed with which it rotate

(c) Moment of inertia of a body about an axis passing through its centre of mass is zero

(d) Moment of inertia of a body depends upon the distribution of mass in the body

Q279. A particle of mass m rotates with a constant speed in XY plane about the Zaxis in a circular path of radius r. Then forthe components of angular momentum (L) of this particle

(a) Lx= 0, Ly= 0, Lz0 (b) Lx= 0, Ly= 0, Lz= 0

(c) Lx0, Ly= 0, Lz= 0 (d) Lx= Ly= Lz= 0

Q280. The radius of gyration of a rod of length about an axis passing through its centre of gravity and perpendicular to its

length is given by


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(a) (b) /2 (c) /3 (d) /2 3

Answers

221. (c): def. center of mass

222. (c): def.

223. (b): def.

224. (c): def.

225. (a) def.

226. (d)

227. (b): def rad of gyration MK2= 2ii rm

228. (a): T = K/I2 I = momentum of inertia

229. (c)

230. (c)

231. (a): KE of rotation = 1/2 I2; v = r232. (a): def.

233. (a) def.

234. (c): def./calculation of Moment of Inertia

235. (a): as above

236. (a): as above def.

237. (b): Torque will be max. at that position

238. (b): Conservation of energy; KE =2

1I2v = n0

239. (a): def.

240. (c): def. of moment of inertia, frictional constant

241. (c)

242. (d) def.

243. (a): def. of MI and equilibrium of force on a moving body

244. (d)

245. (d): calculate tension with given masses246. (b): resultant force balances the frictional force

247. (d): Force time = change of momentum, Torque time = change of Ang. moment248. (d): equilibrium of forces in the helicopter

249. (d): def. of moment of inertia

250. (d): def.

251. (d)

252. (a): accel. Due to motion on curve adds to g to give resultant accl.

253. (b): def. Ang. Mom. = rad vector Force254. (c): def. as above

255. (c): def.

256. (b): conservation of angularmomentum of body and stool

257. (a): conservation KE rotational and potential258. (a): due to centripetal force water will move outward to increase moment of inertia

259. (d): definition of Torque = r F260. (b)

261. (a): outward force will cause increase in the tension

262. (b)

263. (a): r and F are along the same line so r F = 0264. (c): def. r and p are 1 each other

265. (d): def. area swept/ time taken


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266. (d): v = r dt

dv

dt

dv

dt

dv += = red acel + ? acel.

267. (c): def. of ang. Velocitysign convention of direction.268. (c): as above

269. (b):dt

Ld

= torque def.

270. (c): if F = 0, torque will also be zero

271. (a): perpendicular axis ? of MI

272. (c): def. distribution of mass about rotation axis is different

273. (c)

274. (a): Tension is because of the centripetal force

275. (c): def. of linear velocity for circular motion

276. (c)

277. (c): Parallel axis ? of MI

278. (d): definition

279. (a): def. angular momentum

280. (a): def.

rotational motion qns

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