Advertisements
Advertisements
Question
A coin placed on a rotating turntable just slips. If it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of
Options
1 cm
2 cm
4 cm
8 cm
Advertisements
Solution 1
8 cm
Solution 2
1 cm
Let the force of friction between the coin and the rotating turntable be F.
For the coin to just slip ,
we have : \[\text{ F = m }\omega^2 \text{r}\]
Here, \[\text{ m } \omega^2 \text{ r}\] is the centrifugal force acting on the coin.
For constant F and m, we have : \[\text{r} \propto \frac{1}{\omega^2}\]
Therefore,
\[\frac{\text{r}'}{\text{r}} = \left( \frac{\omega}{\omega'} \right)^2 \]
\[ \Rightarrow \text{ r' = 1 cm }\]
APPEARS IN
RELATED QUESTIONS
A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?
A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for `omega <= sqrt(g/R)` .What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for `omega = sqrt("2g"/R)` ?Neglect friction.
A car moves at a constant speed on a road as shown in figure. The normal force by the road on the car NA and NB when it is at the points A and B respectively.
If the earth stop rotating, the apparent value of g on its surface will
A simple pendulum having a bob of mass m is suspended from the ceiling of a car used in a stunt film shooting. the car moves up along an inclined cliff at a speed v and makes a jump to leave the cliff and lands at some distance. Let R be the maximum height of the car from the top of the cliff. The tension in the string when the car is in air is
An object follows a curved path. The following quantities may remain constant during the motion
(a) speed
(b) velocity
(c) acceleration
(d) magnitude of acceleration.
A particle is going in a spiral path as shown in figure with constant speed.
A person stands on a spring balance at the equator. By what fraction is the balance reading less than his true weight?
A turn of radius 20 m 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 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 θ with the vertical. The block rotates with the bowl without any slipping. The friction coefficient between the block and the bowl surface is μ. Find the range of the angular speed for which the block will not slip.
A particle is projected with a speed u at an angle θ with the horizontal. Consider a small part of its path near the highest position and take it approximately to be a circular arc. What is the radius of this circular circle? This radius is called the radius of curvature of the curve at the point.
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 θ/2 with the horizontal?
When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select the correct statement about the directions of its angular velocity and angular acceleration.
Choose the correct option.
Select correct statement about the formula (expression) of moment of inertia (M.I.) in terms of mass M of the object and some of its distance parameter/s, such as R, L, etc.
Two identical masses are connected to a horizontal thin (massless) rod as shown in the figure. When their distance from the pivot is D, a torque τ produces an angular acceleration of α1. The masses are now repositioned so that they are 2D from the pivot. The same torque produces an angular acceleration α2 which is given by ______
A wheel is subjected to uniform angular acceleration about its axis. The wheel is starting from rest and it rotates through an angle θ1, in first two seconds. In the next two seconds, it rotates through an angle θ2. The ratio θ1/θ2 is ____________.
The real force 'F' acting on a particle of mass ' m' performing circular motion acts along the radius of circle 'r' and is directed towards the centre of circle. The square root of the magnitude of such force is (T = periodic time).
A particle performs uniform circular motion in a horizontal plane. The radius of the circle is 10 cm. If the centripetal force F is kept constant but the angular velocity is halved, the new radius of the path will be ______.
A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is `sqrt(x("u"^2 - "gL")`. The value of x is ______.
