Friction and Vertical Circular Motion Problems

Q. 66.A vehicle is moving on a track with constant speed as shown in figure. The apparent weight

Q. Which of the following ( if mass and radius are assumed to be same ) have maximum percentage of total K.E. in rotational form while pure rolling ? ( 1 ) Disc ( 2 ) Sphere ( 3 ) Ring ( 4 ) Hollow sphere

Q. 5. A bead can slide on a smooth straight wire and a particle of mass m attached to the bead by a light stringof length L. The particle is held in contact with the wire and with the string taut and is then let fall. If thebead has mass 2m then when the string makes an angle 0 with the wire, the bead will have slipped a distance

Q.

A 0.10 kg block oscillates back and forth along a horizontal surface. Its displacement from the origin is given by: $x=\left(10cm\right)cos\left[\right(10rads)t+\frac{\pi }{2}rad]$ . What is the maximum acceleration experienced by the block

[AMU (Engg.) 2000]

1. 

2. 

3. 

4. 

Q.

A 2 kg block is lying on a smooth table which is connected by a body of mass 1 kg by a string which passes through a pulley. The 1 kg mass is hanging vertically. The acceleration of block and tension in the string will be

1. 

2. 

3. 

4. 

Q. I-6. A uniform solid sphere of radius R is placed on a smooth horizontal surface. tis pulled by force acting along the tangent from the highest point. Calculate the distance travelled byth mass of the solid sphere during the time it makes one full revolution. e centre of

Q. a wire of mass m and length l is bent in the form of an arc of a circle subtends an angle theta at its centre.relation between MOI about an axis through centre of circle and normal to plane of the circle and angle theta is

Q. Six point masses of mass m each are placed at the vertices of a regular hexagon of side l . calculate the force on any of the masses

Q. { A small object of mass }m, at the end of a light cord, is held horizontally at a distance }r from a fixed support as }} shown. The object is then released. What is the tension in the cord when the object is at the lowest point of its } shing?

Q. A uniform solid cylinder rolling with angular velocity ω along a plane surface strikes a vertical rigid wall. With what angular velocity the cylinder begins to roll up the wall because of impulsive blow? 1) ω/2 2) ω/3 3) ω/4 4) ω/5

Q. A ball of mass $m$ is dropped from a height $h$ equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Choose the correct options. (Mass of earth $=M$)

1. Particle passes the centre of earth with a speed of $\sqrt{\frac{2GM}{R}}$
2. Motion of the particle is periodic
3. Particle will oscillate through the earth to a height $h$ on both sides
4. Particle will execute simple harmonic motion.

Q. a particle of mass m moving with speed u collides elastically with a sphere of radius R and same mass , at rest, at an impact parameter d.find (a) angle between their final velocities and (b)magnitude of their final velocities.

Q.

why does a cyclist lesn inward while negotiating a curve ? Explain with diagram.

Q. 3)RSN4A roller coaster is designed such that ridersexperience "weightlessness" as they go round thetop of a hill whose radius of curvature is 20 m. Thespeed of the car at the top of the hill is between\lbrack AIPMT (Prelims)-2008\rbrack(1) 13 m/s and 14 m/s (2) 14 m/s and 15 m/s3) 15 m/s and 16 m/s (4) 16 m/s and 17 m/s

Q. A body is allowed to slide on a frictionless track from rest position under gravity. The track ends into a circular loop of diameter $D$. What should be the minimum height of the body in terms of $D$ so that it may complete the loop successfully?

1. $\frac{4}{5}D$
2. $\frac{5}{4}D$
3. $1D$
4. $2D$

Q. A bob attached to a light string is rotating in a vertical circle of radius $5\text{m}$. If the velocity of the bob at its lowest point is twice the velocity of the bob when it makes an angle of ${90}^0$ with the vertical. Will the bob complete a full circle? If yes, what is the velocity of the bob at its highest point?

1. The bob will not complete the full circle.
2. The bob will complete the circle and the velocity at the highest point will be $9.12\text{m/s}$.
3. The bob will complete the circle and the velocity at the highest point will be $5.77\text{m/s}$.
4. The bob will complete the circle and the velocity at the highest point will be $7.87\text{m/s}$.

Q.

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig. 9.15. The cross-sectional areas of wires A and B are 1.0 mm² and 2.0 mm², respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.

Q. 2. A particle of mass M rotates in a circle of radius a with uniform angular speed W. it is viewed from a frame rotating with a uniform angular speed W^°. the centrifugal force on the particle is:

Q.

A motorcycle is going on an over-bridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the over-bridge, the normal force on it

1. Decreases

2. Remains the same

3. Fluctuates

4. Increases

Q. A mass of 2 kg is whirled in a circle in a horizontal plane, at an initial speed of 5 revolutions per min. Keeping the radius constant, the speed is increased, so that the centripetal force is four times the initial value. The ratio of the final speed to initial speed is ------

Q. A string attached to a light thread is whirled in a vertical circle with a constant velocity $v$. The radius of the circle is $10\text{m}$. The maximum and minimum tension of the string is in the ratio $4:1$. What is the value of velocity $v$?
(Take $g=10{\text{m/s}}^2$)

1. $15.1\text{m/s}$
2. $13.5\text{m/s}$
3. $12.9\text{m/s}$
4. $10.9\text{m/s}$

Q. A mass $m$ attached to a thin wire is whirled in a vertical circle with a constant speed. The wire is most likely to break when

1. the mass is at the highest point.
2. the wire is horizontal.
3. the mass is at the lowest point.
4. inclined at an angle of $60°$ from vertical.