A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle.
Question types
Circular Motion question types
40 questions across 5 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
40
Questions
5
Question groups
5
Question types
01
1 Marks Question
3 Q→022 Marks Questions
8 Q→033 Marks Question
14 Q→044 Marks Question
5 Q→055 Marks Questions
10 Q→Sample Questions
Circular Motion questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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A scooter weighing 150kg together with its rider moving at 36km/ hr is to take a turn of radius 30m. What horizontal force on the scooter is needed to make the turn possible?
Is it necessary to express all angles in radian while using the equation $\omega=\omega_0+\text{at}?$
View full solution →The bob of a simple pendulum of length 1m has mass 100g and a speed of 1.4m/s at the lowest point in its path. Find the tension in the string at this instant.
A park has a radius of 10m. If a vehicle goes round it at an average speed of 18km/ hr, what should be the proper angle of banking?
A circular road of radius 50m has the angle of banking equal to 30°. At what speed should a vehicle go on this road so that the friction is not used?
A smooth block loosely fits in a circular tube placed on a horizontal surface. The block moves in a uniform circular motion along the tube (figure). Which wall (inner or outer) will exert a nonzero normal contact force on the block?
You are driving a motorcycle on a horizontal road. It is moving with a uniform velocity. Is it possible to accelerate the motoreyle without putting higher petrol input rate into the engine?
Suppose the bob of the previous problem has a speed of 1.4m/ s when the string makes an angle of 0.20 radian with the vertical. Find the tension at this instant. You can use $\cos\theta\approx1-\frac{\theta^2}{2}$ and $\sin\theta\approx\theta$ for small $\theta.$
View full solution →A particle moves in a circle of radius 1.0cm at a speed given by v = 2.0t where v is in cm/s and t in seconds.
- Find the radial acceleration of the particle at t = 1s.
- Find the tangential acceleration at t = 1s.
- Find the magnitude of the acceleration at t = 1s.
What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle $\frac{\theta}{2}$ with the horizontal?
View full solution →A mosquito is sitting on an L.P. record disc rotating on a turn table at $33\frac{1}{3}$ revolutions per minute. The distance of the mosquito from the centre of the turn table is 10cm. Show that the friction coefficient between the record and the mosquito is greater than $\frac{\pi^2}{81}.$ Take g =10 m/s2.
View full solution →A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10m at a speed of 36km/ h. Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turn. Take g= 10m/s2.
A bird while flying takes a left turn, where does it get the centripetal force from?
Some washing machines have cloth driers. It contains a drum in which wet clothes are kept. As the drum rotates, the water particles get separated from the cloth. The general description of this action is that "the centrifugal force throws the water particles away from the drum". Comment on this statement from the viewpoint of an observer rotating with the drum and the observer who is washing the clothes.
A car driver going at some speed v suddenly finds a wide wall at a distance r. Should he apply brakes or turn the car in a circle of radius r to avoid hitting the wall?
A small coin is placed on a record rotating at $33\frac{1}{3}$ rev/ minute. The coin does not slip on the record. Where does it get the required centripetal force from?
View full solution →After a good meal at a party you wash your hands and find that you have forgotten to bring your handkerchief. You shake your hands vigorously to remove the water as much as you can. Why is water removed in this process?
A person stands on a spring balance at the equator.
- By what fraction is the balance reading less than his true weight?
- If the speed of earth's rotation is increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case?
A turn of radius 20m is banked for the vehicles going at a speed of 36 km/h. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up?
A track consists of two circular parts ABC and CDE of equal radius 100m and joined smoothly as shown in figure. Each part subtends a right angle at its centre. A cycle weighing 100 kg together with the rider travels at a constant speed of 18km/h on the track.
- Find the normal contact force by the road on the cycle when it is at B and at D.
- Find the force of friction exerted by the track on the tyres when the cycle is at B, C and D.
- Find the normal force between the road and the cycle just before and just after the cycle crosses C.
- What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take g= 10m/s2.
A hemispherical bowl of radius R is rotated about its axis of symmetry which is kept vertical. A small block is kept in the bowl at a position where the radius makes an angle $\theta$ with the vertical. The block rotates with the bowl without any slipping. The friction coefficient between the block and the bowl surface is $\mu.$ Find the range of the angular speed for which the block will not slip.
View full solution →A block of mass m moves on a horizontal circle against the wall of a cylindrical room of radius R. The floor of the room on which the block moves is smooth but the friction coefficient between the wall and the block is $\mu.$ The block is given an initial speed $\nu_0.$ As a function of the speed $\nu$ write,
View full solution →- The normal force by the wall on the block.
- The frictional force by the wall.
- The tangential acceleration of the block.
- Integrate the tangential acceleration $\Big(\frac{\text{d}\nu}{\text{dt}}=\nu\frac{\text{d}\nu}{\text{ds}}\Big)$ to obtain the speed dt ds of the block after one revolution.
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