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.
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Circular Motion question types
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2 Marks Questions
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14 Q→031 Marks Question
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5 Q→055 Marks Questions
10 Q→Sample Questions
Circular Motion questions
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If the road of the previous problem is horizontal (no banking),The road is horizontal (no banking) what should be the minimum friction coefficient so that a scooter going at 18km/hr does not skid?
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 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?
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 →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 →In a children's park a heavy rod is pivoted at the centre and is made to rotate about the pivot so that the rod always remains horizontal. Two kids hold the rod near the ends and thus rotate with the rod (fig). Let the mass of each kid be 15 kg, the distance between the points of the rod where the two kids hold it be 3.0 m and suppose that the rod rotates at the rate of 20 revolutions per minute. Find the force of friction exerted by the rod on one of the kids.
A table with smooth horizontal surface is placed in a cabin which moves in a circle of a large radius R (figure In). A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the strings along the outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the masses as seen from the cabin and the tension in the string.
Consider the circular motion of the earth around the sun. Which of the following statements is more appropriate?
- Gravitational attraction of the sun on the earth is equal to the centripetal force.
- Gravitational attraction of the sun on the earth is the centripetal force.
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 →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.
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?
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 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 →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 bird while flying takes a left turn, where does it get the centripetal force from?
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.
A car moving at a speed of 36 km/hr is taking a turn on a circular road of radius 50m. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (figure In). A small block of mass 100g is kept on the seat which rests against the plate. The friction coefficient between the block and the plate is $\mu=0.58.$
View full solution →- Find the normal contact force exerted by the plate on the block.
- The plate is slowly turned so that the angle between the normal to the plate and the radius of the road slowly increases. Find the angle at which the block will just start sliding on the plate.
A motorcycle has to move with a constant speed on an overbridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point.
View full solution →- What can its maximum velocity be for which the contact with the road is not broken at the highest point?
- If the motorcycle goes at speed $\frac{1}{\sqrt2}$ times the maximum found in part (a), where will it lose the contact with the road?
- What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?
A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity $\omega$ in a circular path of radius R (In figure). A smooth groove AB of length L(<<R) is made on the surface of the table. The groove makes an angle $\theta$ with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move along AB. Find the time taken by the particle to reach the point B.
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