If a particle moves in a circle describing equal angles in equal times, its velocity vector:
(1) remains constant.
(2) changes in magnitude.
(3) changes in direction.
(4) changes both in magnitude and direction.
A motorcyclist going round in a circular track at constant speed has:
(1) constant linear velocity
(2) constant acceleration
(3) constant angular velocity
(4) constant force
A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B, the angular velocity of P about A and C are in the ratio
(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 4 : 1
The angular speed of a fly wheel making \(120\) revolutions/minute is:
1. \(2\pi~\mathrm{rad/s}\)
2. \(4\pi^2~\mathrm{rad/s}\)
3. \(\pi~\mathrm{rad/s}\)
4. \(4\pi~\mathrm{rad/s}\)
Certain neutron stars are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be:
1. | \(20 \times 10^8 \mathrm{~m} / \mathrm{s}^2 \) | 2. | \(8 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) |
3. | \(120 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) | 4. | \(4 \times 10^8 \mathrm{~m} / \mathrm{s}^2\) |
An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m, the acceleration of a point on the tip of the blade is about
(1) 1600 m/sec2
(2) 4740 m/sec2
(3) 2370 m/sec2
(4) 5055 m/sec2
If ar and at represent radial and tangential accelerations, the motion of a particle will be uniformly circular if
1. ar = 0 and at = 0
2. ar = 0 but
3. but at = 0
4. and
In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m (see figure). The magnitude of the average velocity is:
1. | 3.14 m/s | 2. | 2.0 m/s |
3. | 1.0 m/s | 4. | Zero |
The coordinates of a moving particle at any time \(t\) are given by \(x=\alpha t^3\) and \(y=\beta t^3.\) The speed of the particle at time \(t\) is given by:
1. \(\sqrt{\alpha^2+\beta^2}~\)
2. \(3t\sqrt{\alpha^2+\beta^2}~\)
3. \(3t^2\sqrt{\alpha^2+\beta^2}~\)
4. \(t^2\sqrt{\alpha^2+\beta^2}~\)
Figure shows a body of mass m moving with a uniform speed v along a circle of radius r. The change in velocity in going from A to B is
(1)
(2)
(3) v
(4) zero