Instantaneous Axis of Rotation

Q. an insect trapped in a circular groove of radius 12cm moves along the groove steadily and comppetes 7 revolution in 100s what is the magnitude of centripetal acceleration in above problem

Q. A disc rotating about its axis with angular speed wo is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated ?

Q. a motorcycle is moving in a circular path of radius 10m and with uniform speed 36km/h the angle with vertical at which motorcyclist will bend is

Q.

The angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:

1. 40 radian/s

2. 20 radian/s

3. 10 radian/s

4. 30 radian/s

Q. 34.A river flows at 3 metre per second and is 300 metre wide. A man Swims across the river with a velocity of 2 metre per second directed always perpendicular to the flow of current. (i)how long does it take the man to cross the river ?(ii) in what direction does he actually move relative to the shore? (iii) how far down the stream (from the starting point) does he reach the opposite bank?

Q. A sphere is rolling without slipping with velocity V, on a thin plank moving with 3V, as showin figure. Find distance of instantanous axis of rotation from centre of sphere. velocity of cm sphere is towards right abd velocity of plank is towards le

Q. A body rolls down a staircase of 5 steps.each step has height 0.1 m and width 0.1 m .With what velocity will the body reach bottom?

Q. 49.A particle is projected with a velocity u at an angle (theta) with the horizontal. Find the radius of curvature of the parabola traced out by the particle at the point where its velocity makes an angle (theta/2) with the horizontal.

Q. 8. The distance traveled by a body starting from restand travelling with uniform acceleration, insuccessive intervals of time of equal duration will bein the ratio

Q. A ball of mass 0.5 kg is moved in a vertical circle. When ball is at P then calculate its tangential acceleration.

Q. A point P consider at contact point of a wheel on ground which rolls on the ground without slipping then value of displacement of point P when wheel complets half of rotation (If radius of wheel is 1 m )

Q. A particlr moves along the curve x2/9+y2/4=1with cons†an t speed v.Express its velocity vectorially as a functionof(x, y

Q. A sphere of masss m and radius r rolls without slipping on a rough concave surface of large radius R .It makes small oscillations about the lowest point .Find time period .

Q.

A body is rolling down an inclined plane without slipping. How does the acceleration of the rolling body depend on its radius?

1. It is directly proportional to the square root of radius

2. It is inversely proportional to the square root of radius

3. It does not depend upon radius

4. It is directly proportional to the radius

Q. A particle moves an a straight line with a constanacceleration. t changes its velocity firom 10 mso 20 ms while passing through a distanc135 m in f second. The value of t isAIPMT (Prelims)-200(2) 106 (@l(3) 1.8(4) 12

Q. 108.A wheel is rolling without slipping on a straight road find the magnitude of displacement of point P when it rolls down at 1.5 turns and point p is in contact with the ground

Q.

Two spheres made of same material have radii r and 2r. They are initially touching each other and start moving out along the line joining their centres with velocities 4v and v respectively. The velocity of their centre of mass is

1. 4v/3 in the direction of motion of larger sphere

2. 4v/9 in the direction of motion of larger sphere

3. 4v/9 in the direction of motion of smaller sphere

4. zero

Q. Assertion :- During circular motion centripetal acceleration remains cons†an t. Reason :- Magnitude of centripetal acceleration is given as Image not present.

Q.

The angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:

1. 20 radian/s

2. 30 radian/s

3. 40 radian/s

4. 10 radian/s

Q. the dis†an ce of a particle moving on a circle of radius 12m measured from a fixed point on the circle is given by s=2t^{3 }the ratio of †an gential to centripetal acceleration is

Q. Q. A partical moving with a uniform accleration travels 24 meters and 64 meters in first two successive intervals of 4 second each. its initial velocity is?

Q. a particle moves along the curve given by x=t , y=(t^2)/2 (when time=t). find the magnitude of centripetal acceleration when t=1

Q. of radius r and mass m rotating with anangular velocity oo is placed on a rough horizontalce. The initial velocity of the centre of the hoopis zero. What will be the velocity of the centre of thehoop when it ceases to slip? \lbrack JEE (Main)-20134) A hoopsurfa(2) 10roo(3) 2(4) Wglors strina

Q. A rigid body is rotating with variable angular velocity ω = (28 – 4t) radian/s, the total angle rotated by it before coming to rest will be
(1) 98 radians
(2) 96 radians
(3) 196 radians
(4) 94 radians

Q. Two cars move uniformly towards each other. Theybecome 6 m nearer in every 2 second and they get4 m closer in every 8 second, if they move in onesame direction with their previous speeds. Thespeeds of the cars are

Q. The stick applies a force of $2\text{N}$ on the ring$(R=0.5\text{m})$ and the ring rolls without slipping on the ground as shown in figure. The coefficient of friction between the stick and the ring is

1. $0.4$
2. $0.3$
3. $0.2$
4. $0.5$

Q. 80. A particle is given vertical velocity and passes a height h two times in its journey at 4 sec and 9 sec respectively. Find the height h?

Q. Two swimmers leave. A on one bank of the river to reach point B line right across the other back one of the two causes the river along the straight line AB while the other streams at right angle to the stream and then whats the distance that he has been carried away by the street to get to point B. What is the velocity of his walking if both swimmers reached the destination simultaneously? ( The stream velocity = 2 km/h and the velocity of each swimmer w.r.t still water is 2.5 km/h)

Q. Wheel is at rest, its angular velocity increases uniformsly and becomes 60 rad s-1 after 5 secs. Calculate the total angular displacement.

Q. 4. A man can swim at the rate of 4 km/h in stillwater. A 500 m wide river flows at the rate of3 km/h. If the man keep his alignmentperpendicular to the river flow then time takenby man to cross the river is(1) 10 minute(2) 5 minute(3) 15 minute(4) 7.5 minute