In the uniform circular motion, which of the following physical quantity remains constant?

(1) Angular velocity

(2) Angular momentum

(3) Angular speed

(4) All of these

A body is projected with velocity $\overrightarrow{\mathrm{v}}= \left(\mathrm{\alpha }\hat{\mathrm{i}} + \mathrm{\beta }\hat{\mathrm{j}}\right)$ m/s. The time of flight of body considering x as horizontal and y as the vertical axis and g is the acceleration due to gravity:

1.  $\frac{2\mathrm{\beta }}{\mathrm{g}}$

2.  $\frac{2\mathrm{\alpha }}{\mathrm{g}}$

3.  $\frac{2\mathrm{\alpha \beta }}{\mathrm{g}}$

4.  $\frac{2\mathrm{\alpha }}{\mathrm{g\beta }}$

Two balls are projected along the same initial line from a height h = 20 m. The direction of the projections is horizontal. If initial speeds are 20 m/s and 25 m/s, the maximum separation between the balls when they will hit the ground is

(1) 40 m

(2) 50 m

(3) 10 m

(4) 90 m

If the position of a particle varies according to the equations \(x= 3t^2\)${\mathrm{}}^{}$, \(y =2t\), and \(z= 4t+4\), then which of the following is incorrect?

If three coordinates of a particle change according to the equations \(x = 3 t^{2}, y = 2 t , z= 4\), then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. \(2\sqrt{11}~\text{unit}\)
2. \(\sqrt{34}~\text{unit}\)
3. \(40~\text{unit}\)
4. \(2\sqrt{10}~\text{unit}\)

Two bodies of equal masses are projected, one from top of the tower in the horizontal direction and other from the foot of tower at an angle of 45° with the horizontal, then the acceleration of their center of mass is

(1) $\frac{\mathrm{g}}{\sqrt{2}}$downward

(2) g downward

(3) $\frac{\mathrm{g}\left(\sqrt{2} - 1\right)}{\sqrt{2}}$ downward

(4) $\frac{\mathrm{g}\left(\sqrt{2} + 1\right)}{\sqrt{2}}$ upward

A projectile is projected at an angle of 60° from horizontal. At an instant, it is moving at an angle of 30° with horizontal with velocity 10 m/s. The radial acceleration of the particle at that instant is:

1.  $\frac{20}{\sqrt{2}}\mathrm{m}/{\mathrm{s}}^2$

2.  $\frac{20}{\sqrt{3}}\mathrm{m}/{\mathrm{s}}^2$

3.  $20\sqrt{3}\mathrm{m}/{\mathrm{s}}^2$

4.  $5\sqrt{3}\mathrm{m}/{\mathrm{s}}^2$

The initial velocity of a projectile is given by $\mathrm{v} = \left(20\hat{\mathrm{i}} + 50\hat{\mathrm{j}} + 70\hat{\mathrm{k}}\right)$ m/s. If acceleration due to gravity is g = 10($-\hat{\mathrm{k}}$) m/${\mathrm{s}}^2$, then the time after which projectile returns to the same horizontal level is:

(1) 4 s

(2) 10 s

(3) 14 s

(4) 12 s

Two persons start moving along two crossroads with the same speed 5 m/s. One in the direction of north and other is in the direction of the east as shown in the figure. Angular velocity of A with respect to B is :

(1) 0.5 m/s

(2) Zero

(3) 1.0 m/s

(4) 2 m/s

In projectile motion, accelerations of the projectile when it is gaining height and losing height respectively are

(1) g upward, g upward

(2) g upward, g downward

(3) g downward, g downward

(4) g downward, g upward