A sprinkler is deployed to irrigate the garden. The speed of water-jet from the sprinkler is u. The maximum area which can be irrigated by the sprinkler is

1.  $\frac{{\mathrm{\pi }}^2{\mathrm{u}}^2}{\mathrm{g}}$

2.  $\frac{{\mathrm{\pi u}}^2}{\mathrm{g}}$

3.  $\frac{{\mathrm{\pi u}}^2}{{\mathrm{g}}^2}$

4.  $\frac{{\mathrm{\pi u}}^4}{{\mathrm{g}}^2}$

Which of the following is an appropriate expression for the radius of curvature of a projectile at the highest point? (R $\to$ Range of projectile)

(1) $\frac{\mathrm{R}}{2} \cot \mathrm{\theta }$

(2) $\frac{\mathrm{R}}{2} \tan \mathrm{\theta }$

(3) 2R cot $\mathrm{\theta }$

(4) 2R tan $\mathrm{\theta }$

The coordinates of a particle moving in the x-y plane vary with time according to the following relation:

$\mathrm{x} = \frac{\mathrm{B}}{\mathrm{t}}$, $\mathrm{y} = \mathrm{A}\sqrt{\mathrm{t}}$.

The locus of the particle is:

(1) Parabola

(2) Circle

(3) Eclipse

(4) Hyperbola

If ${\mathrm{t}}_1$ represents the instant at which the instantaneous velocity becomes perpendicular to the direction of initial velocity during a projectile and ${\mathrm{t}}_2$ represents the time after which the particle attains maximum height, then $\sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}$ is:

1.  $\frac{\mathrm{u}}{\mathrm{g}}$

2.  $\frac{2\mathrm{u}}{\mathrm{g}}$

3.  $\frac{\mathrm{u}}{2\mathrm{g}}$

4.  $\frac{\mathrm{u} {\sin }^2 \mathrm{\theta }}{\mathrm{g}}$

A park is in the shape of a regular hexagon. Six friends standing at each corner of the park start moving towards each other with the same speed 2 m/s and meet each other after 60 s. The side of the park is

(1) 120 m

(2) 30 m

(3) 240 m

(4) 60 m

A ball is projected horizontally from a cliff 40 m high at a speed of 40 m/s and simultaneously a ball is dropped. If the time taken by the two balls to reach the ground are ${\mathrm{t}}_1 \mathrm{and} {\mathrm{t}}_2$ respectively (taking air friction into consideration), then

(1) ${\mathrm{t}}_1 > {\mathrm{t}}_2$

(2) ${\mathrm{t}}_1 < {\mathrm{t}}_2$

(3) ${\mathrm{t}}_1 = {\mathrm{t}}_2$

(4) Depending on air friction ${\mathrm{t}}_1$ maybe less or more than ${\mathrm{t}}_2$

 Select the incorrect statement:

A projectile is fired horizontally from the top of a tower. The time after which the instantaneous velocity will be perpendicular to the initial velocity is (neglect air resistance) :

(1) $\mathrm{t} = \frac{\mathrm{u} \sin \mathrm{\theta }}{\mathrm{g}}$

(2) $\mathrm{t} = \frac{\mathrm{u}}{\mathrm{g} \sin \mathrm{\theta }}$

(3) $\mathrm{t} = \frac{\mathrm{u}}{\mathrm{g} \cos \mathrm{\theta }}$

(4) It will never be perpendicular at any instant

A particle of mass 2 kg is moving in a circular path with a constant speed of 10 m/s. The change in the magnitude of velocity when a particle travels from P to Q will be: [assume the radius of the circle is 10/${\mathrm{\pi }}^2$]
         

Uniform circular motion is an example of:

(1) Uniform motion

(2) Uniform speed

(3) Uniform acceleration

(4) Non-uniform speed