Advertisements
Advertisements
प्रश्न
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 (In the following figure). 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.
Advertisements
उत्तर
Given :
\[\text {Frequency of rod }= n = 20 \text{ rev} \text{ per } \min\]
\[ \Rightarrow \text{ n} = \frac{20}{60} = \frac{1}{3}\text{rev/s}\]
Therefore, we have :
angular velocity of rod ,
\[\text { Angular velocity of rod }= \omega = 2\pi n = \frac{2\pi}{3}\text{rad/s}\]
Mass of each kid = \[\text{m = 15 kg}\]
Radius = \[r = \frac{3}{2} = 1 . 5 \text{m}\]
\[\therefore \text { Frictional force }= F = \text{mr }\omega^2 \]
\[ \Rightarrow F = 15 \times (1 . 5) \times \frac{(2\pi )^2}{9}\]
\[ = 5 \times (0 . 5) \times 4 \pi^2 = 10 \pi^2 N\]
Thus, the force of frictional on one of the kids is 10 \[\pi\]
APPEARS IN
संबंधित प्रश्न
Tow cars having masses m1 and m2 moves in circles of radii r1 and r2 respectively. If they complete the circle in equal time, the ratio of their angular speed ω1/ω2 is
A train A runs from east to west and another train B of the same mass runs from west to east at the same speed along the equator. A presses the track with a force F1 and B presses the track with a force F2.
A car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is v and is increasing at a rate a.
(a) The acceleration of the car is towards the centre of the path.
(b) The magnitude of the frictional force on the car is greater than \[\frac{\text{mv}^2}{\text{r}}\]
(c) The friction coefficient between the ground and the car is not less than a/g.
(d) The friction coefficient between the ground and the car is \[\mu = \tan^{- 1} \frac{\text{v}^2}{\text{rg}.}\]
Find the acceleration of a particle placed on the surface of the earth at the equator due to earth's rotation. The diameter of earth = 12800 km and it takes 24 hours for the earth to complete one revolution about its axis.
A scooter weighing 150 kg together with its rider moving at 36 km/hr is to take a turn of a radius 30 m. What horizontal force on the scooter is needed to make the turn possible ?
A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of 120 cm and rpm 1500 at full speed. Consider a particle of mass 1 g sticking at the outer end of a blade. How much force does it experience when the fan runs at full speed? Who exerts this force on the particle? How much force does the particle exert on the blade along its surface?
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.
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?
A car moving at a speed of 36 km/hr is taking a turn on a circular road of radius 50 m. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (In the following figure). A small block of mass 100 g is kept on the seat which rests against the plate. the friction coefficient between the block and the plate is. (a) Find the normal contact force exerted by the plate on the block. (b) 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 particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform the vertical circular motion, under gravity. The minimum speed of a particle is 5 m/s. Consider the following statements.
P) Maximum speed must be `5sqrt5` m/s.
Q) Difference between maximum and minimum tensions along the string is 60 N.
Select the correct option.
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.
Choose the correct option.
Consider the following cases:
(P) A planet revolving in an elliptical orbit.
(Q) A planet revolving in a circular orbit.
Principle of conservation of angular momentum comes in force in which of these?
A particle is moving in a radius R with constant speed v. The magnitude of average acceleration after half revolution 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).
The centripetal force of a body moving in a circular path, if speed is made half and radius is made four times the original value, will ____________.
Angular displacement (θ) of a flywheel varies with time as θ = at + bt2 + ct3 then angular acceleration is given by ____________.
If a cyclist doubles his speed while negotiating a curve, how does the tendency to overturn vary?
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 body is moving along a circular track of radius 100 m with velocity 20 m/s. Its tangential acceleration is 3 m/s2 then its resultant accelaration will be ______.
Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?
