If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if 

1. a_r = 0 and a_t = 0

2. a_r = 0 but $a_t\ne 0$

3. $a_r\ne 0$ but a_t = 0

4. $a_r\ne 0$ and $a_t\ne 0$

In \(1.0~\text{s}\), a particle goes from point \(A\) to point \(B\), moving in a semicircle of radius \(1.0~\text{m}\) (see figure). The magnitude of the average velocity is:

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) $v\sqrt{2}$

(2) $v/\sqrt{2}$

(3) v

(4) zero

The angle turned by a body undergoing circular motion depends on the time as given by the equation, \(\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}\). It can be deduced that the angular acceleration of the body is? 
1. \(\theta_1\)
2. \(\theta_2\)
3. \(2\theta_1\)
4. \(2\theta_2\)

An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

(1) On a parabolic path as seen by pilot in the plane

(2) Vertically along a straight path as seen by an observer on the ground near the target

(3) On a parabolic path as seen by an observer on the ground near the target

(4) On a zig-zag path as seen by pilot in the plane

A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is 

(1) ${25}^o{8}^{\text{'}}$

(2) ${33}^o{7}^{\text{'}}$

(3) ${42}^o{8}^{\text{'}}$

(4) ${53}^o{8}^{\text{'}}$

Two bodies are projected with the same velocity. If one is projected at an angle of 30° and the other at an angle of 60° to the horizontal, the ratio of the maximum heights reached is 

(1) 3 : 1

(2) 1 : 3

(3) 1 : 2

(4) 2 : 1

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is 

(1) 100 m

(2) 80 m

(3) 60 m

(4) 50 m

A particle is moving eastwards with velocity of \(5\) m/s. In \(10\) seconds the velocity changes to \(5\) m/s northwards. The average acceleration in this time is?