Advertisements
Advertisements
Question
A person stands on a spring balance at the equator. By what fraction is the balance reading less than his true weight?
Solution
Balance reading = Normal force on the balance by the Earth.
At equator, the normal force (N) on the spring balance :
N = mg − mω2r
True weight = mg
Therefore, we have :
\[\text { Fraction less than the true weight } = \frac{\text{mg - (mg - m }\omega^2 r)}{\text{mg}}\]
\[ = \frac{\omega^2 r}{g} = \left( \frac{2\pi}{24 \times 3600} \right)^2 \left( \frac{6 . 4 \times {10}^6}{10} \right)\]
\[= 3 . 5 \times {10}^{- 3}\]
APPEARS IN
RELATED QUESTIONS
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.
Water in a bucket is whirled in a vertical circle with string attached to it. The water does no fall down even when the bucket is inverted at the top of its path. We conclude that in this position
A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it
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.
The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time. Its
(a) velocity remains constant
(b) speed remains constant
(c) acceleration remains constant
(d) tangential acceleration remains constant.
The bob of a simple pendulum of length 1 m has mass 100 g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the string at this instant.
Suppose the amplitude of a simple pendulum having a bob of mass m is θ0. Find the tension in the string when the bob is at its extreme position.
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 motorcycle has to move with a constant speed on an over bridge 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.(a) What can its maximum velocity be for which the contact with the road is not broken at the highest point? (b) If the motorcycle goes at speed 1/√2 times the maximum found in part (a), where will it lose the contact with the road? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?
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.
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.
In non-uniform circular motion, the ratio of tangential to radial acceleration is (r = radius, a = angular acceleration and v = linear velocity)
A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m. What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N? (Cylinder is rotating about its own axis.)
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 acceleration will be ______.
A body of M.I. 2 kg m2 rotates with an angular velocity of 20 rad/s. When an external torque of 0.5 N m acts on it in the opposite direction, the number of revolutions it makes before it comes to rest is ____________.
A person driving a car suddenly applies the brakes on seeing a child on the road ahead. If he is not wearing seat belt, he falls forward and hits his head against the steering wheel. Why?
When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.
A racing car travels on a track (without banking) ABCDEFA (Figure). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is µ = 0.1. The maximum speed of the car is 50 ms–1. Find the minimum time for completing one round.
A racing car is travelling along a track at a constant speed of 40 m/s. A T.V. cameraman is recording the event from a distance of 30 m directly away from the track as shown in the figure. In order to keep the car under view in the position shown, the angular speed with which the camera should be rotated is ______.
