A particle starting from rest moves in a circle of radius 'r'. It attains a velocity of $v_0$ m/s on completion of n rounds. Its angular acceleration will be:

1. $\frac{v_0}{n} rad/s^2$

2. $\frac{v_0^2}{2{\mathrm{\pi nr}}^2} rad/s^2$

3. $\frac{v_o^2}{4{\mathrm{\pi nr}}^2} rad/s^2$

4. $\frac{v_0^2}{4\mathrm{\pi nr}} rad/s^2$

Two bullets are fired horizontally and simultaneously towards each other from rooftops of two buildings (building being 100 m apart and being of the same height of 200 m) with the same velocity of 25 m/s. When and where will the two bullets collide? (g = 10 m/$s^2$)?

1. after 2s at a height of 180 m

2. after 2s at a height of 20 m

3. after 4s at a height of 120 m

4. they will not collide.

Two particles A and B are moving in a uniform circular motion in concentric circles of radii $r_A and r_B$ with speeds $v_A and v_B$ respectively. Their time periods of rotation are the same. The ratio of angular speed of A  to that of B will be:

1. 1: 1

2. $r_A : r_B$

3. $v_A : v_B$

4. $r_B : r_A$

The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to north is given by:

1. 45$°$ west of north

2. 30$°$ west of north

3. 0$°$ west of north

4. 60$°$ west of north

A car turns at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap, respectively, is :

1. 0,0

2. 0, 10 m/s

3. 10 m/s, 10 m/s

4. 10 m/s, 0

For a projectile projected at angles (45°-θ) and (45°+θ), the horizontal ranges described by the projectile are in the ratio of:

1. 1:1

2. 2:3

3. 1:2

4. 2:1

A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are ($\sqrt{3}$, 3). The path of the particle makes an angle of .......................with the x-axis :

1. 30^o

2. 45^o

3. 60^o

4. 0^o

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground, the magnitude of change in its momentum will be:

1.  $2\mathrm{mv}$

2.  $\mathrm{mv}/\sqrt{2}$

3.  $\mathrm{mv}\sqrt{2}$

4.  zero

A particle has initial velocity $(3\hat{\mathrm{i}} + 4\hat{\mathrm{j}})$ and has acceleration $(0.4\hat{\mathrm{i}}+ 0.3\hat{\mathrm{j}})$. Its speed after 10 s is

1. 7 units

2. 7$\sqrt{2}$units

3. 8.5 units

4. 10 units

A missile is fired for a maximum range with an initial velocity of 20 m/s. If g= 10 m/s², then the range of the missile will be

1.  50 m

2.  60 m

3.  20 m

4.  40 m