Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, the tension in the string is mg cosθ
A. always

B. never

C. at the extreme positions

D. at the mean position

The displacement vector of a particle of mass m is given by r (t) = î A cos ωt + ĵ B sin ωt.

(a) Show that the trajectory is an ellipse.

(b) Show that F = −mω²r

A racing car travels on a track (without banking) ABCDEFA (Fig. 5.10). 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 m s^-1. Find the minimum time for completing one round.

A motorcycle is going on an over bridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the over bridge, the normal force on it

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 υ 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

The center of a wheel rolling on a plane surface moves with a speed A particle on the rim of the wheel at the same level as the center will be moving at speed

Water in a bucket is whirled in a vertical circle with a string attached to it. The water does not fall down even when the bucket is inverted at the top of its path. We conclude that in this position

A stone of mass m tied to a string of length I is rotated in a circle with the other end of the string as the center. The speed of the stone is u. If the string breaks, the stone will move

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 car of mass M is moving on a horizontal circular path of radius r. At an instant its speed is υ and is increasing at a rate a.

A person applies a constant force on a particle of mass m and finds that the particle moves in a circle of radius r with a uniform speed u as seen from an inertial frame of reference.