A body moved along x-axis and y-axis according to the equation,

$x=2\sin \theta$
$y=3\cos \theta$

What is the trajectory followed by the body?

1.  

2.  

3.  

4.  

A particle of mass \(m\) is projected with a velocity at an angle with the horizontal into a uniform gravitational field. The slope of the trajectory varies with horizontal distance \(x\) as:

1.		2.
3.		4.

A projectile thrown at an angle 30° with horizontal from the level ground reaches a maximum height of 20 m. What will be the maximum height if it is thrown at an angle 60° with the same speed?

(1) 20 m

(2) 30 m

(3) 50 m

(4) 60 m

A body moving in a uniform circular motion with speed v. The magnitude of the change in its velocity after it rotates by an angle 120° is:
1. \(2v\)
2. \(\sqrt{3}v\)
3. \(v\)
4. \(\frac{\sqrt{3}}{2}v\)

A car moves on a circular path such that its speed is given by v = Kt, where K =constant and t is time. Also given: radius of the circular path is r. The net acceleration of the car at time t will be:

1. $\sqrt{{\mathrm{K}}^2 + {\left(\frac{{\mathrm{K}}^2{\mathrm{t}}^2}{\mathrm{r}}\right)}^2}$

2. 2K

3. K

4. $\sqrt{{\mathrm{K}}^2 + {\mathrm{K}}^2{\mathrm{t}}^2}$

An object of mass 10 kg is projected from level ground with speed 40 m/s at angle 30° with horizontal. The rate of change of momentum of object [in SI units] 1 second after the projection is [neglect air resistance]

(1) 100

(2) 50

(3) 25

(4) 75

A particle is projected horizontally with speed 20 m/s from a cliff of height 20 m. The magnitude of the velocity of particle when it reaches the ground

1. 20 m/s

2. 40 m/s

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

4. Zero

A projectile is thrown with an initial velocity of 20 m/s at an angle of 60° with horizontal, then the angle of the velocity of the projectile with horizontal after time 0.732 sec is:

(1) 45°

(2) 30°

(3) 0°

(4) 15°

If ${\mathrm{a}}_{\mathrm{r}} \mathrm{and} {\mathrm{a}}_{\mathrm{t}}$ represent radial and tangential accelerations, then the motion of particle will be uniformly circular for :

(1) ${\mathrm{a}}_{\mathrm{r}}$ = 0, ${\mathrm{a}}_{\mathrm{t}}$ = 0

(2) ${\mathrm{a}}_{\mathrm{r}}$ = 0, ${\mathrm{a}}_{\mathrm{t}}$ $\ne$ 0

(3) ${\mathrm{a}}_{\mathrm{r}}$ $\ne$ 0, ${\mathrm{a}}_{\mathrm{t}}$ = 0

(4) ${\mathrm{a}}_{\mathrm{r}}$ $\ne$ 0, ${\mathrm{a}}_{\mathrm{t}}$ $\ne$ 0

A helicopter flies from a city A to B. The line joining A and B is along North-South direction and its length is 100 km. The speed of the helicopter is kept 100 km/h and the wind blows from West to East with a speed of 60 km/h. The time taken by the helicopter is

(1) 0.75 h

(2) 1.0 h

(3) 1.25 h

(4) 1.33 h