A particle moves with constant angular velocity in a circle. During the motion its:

1.	Energy is conserved
2.	Momentum is conserved
3.	Energy and momentum both are conserved
4.	None of the above is conserved

What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\)  :

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is:

1. $2$ $\pi$ $v/T$

2. $2$ $\pi$ $r/T$

3. $2$ $\pi$ $r^2/T$

4. $2$ $\pi$ $v^2/T$

If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where θ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is:

1. 8 rad/sec

2. 12 rad/sec

3. 24 rad/sec

4. 36 rad/sec

The coordinates of a moving particle at any time ‘t’ are given by x = αt³ and y = βt³. The speed of the particle at time ‘t’ is given by:

1. $\sqrt{{\alpha }^2+{\beta }^2}$

2. $3$ $t\sqrt{{\alpha }^2+{\beta }^2}$

3. $3$ $t^2\sqrt{{\alpha }^2+{\beta }^2}$

4. $t^2\sqrt{{\alpha }^2+{\beta }^2}$

At the top of the trajectory of a projectile, the directions of its velocity and acceleration are:

Four bodies P, Q, R and S are projected with equal velocities having angles of projection 15^o, 30^o, 45^o and 60^o with the horizontal respectively. The body having the shortest range is? 

A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle $\left(\frac{\pi }{2}-\theta \right)$with the horizontal, it reaches maximum height H₂. The relation between the horizontal range of the projectile R and H₁ & H₂ is: 

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

The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be:

1. 45°

2. 60°

3. 90°

4. 30°