If a particle is moving in a circular orbit with constant speed, then:

1.	its velocity is variable.
2.	its acceleration is variable.
3.	its angular momentum is constant.
4.	All of the above

A body is projected horizontally with speed u from a tower of height h. The magnitude of the velocity with which it will collide with the ground will be: [g is the acceleration due to gravity]

1.  $\sqrt{2\mathrm{gh}}$

2.  $\mathrm{u}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\sqrt{2\mathrm{gh}}$

3.  ${\mathrm{u}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\sqrt{2\mathrm{gh}}$

4.  $\sqrt{{\mathrm{u}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>2\mathrm{gh}}$

The position vector of a particle \(\overrightarrow r\) as a function of time \(t\) (in seconds) is \(\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}\). The initial acceleration of the particle is:
1. \(2~\text{m/s}^2\)
2. \(3~\text{m/s}^2\)
3. \(4~\text{m/s}^2\)
4. zero

Coordinates of a particle as a function of time \(t\) are \(x= 2t\),
\(y =4t\). It can be inferred that the path of the particle will be:

At a certain instant, a particle moving in the \(xy\text-\)plane has a velocity of \(\vec v=(2\hat{i}+3\hat{j})~\text{m/s}\) and an acceleration of \(\vec a=(-3\hat{i}+2\hat{j})~\text{m/s}^2.\) What is the rate of change of the particle’s speed at that instant?
1. \(\sqrt{13}\) m/s²
2. \(-1\) m/s²
3. \(1\) m/s²
4. zero

A body started moving with an initial velocity of \(4\) m/s along the east and an acceleration \(1\) m/s² along the north. The velocity of the body just after \(4\) s will be?

A projectile thrown from the ground has horizontal range R. If velocity at the highest point is doubled somehow, the new range will be:

(1) 3 R

(2) 1.5 R

(3) $\sqrt{3}$ R

(4) 2 R

A particle is projected from the origin with velocity $\left(4\hat{\mathrm{i}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>9\hat{\mathrm{j}}\right)$ m/s. The acceleration in the region is constant and -10$\hat{\mathrm{j}}$ $\mathrm{m}/{\mathrm{s}}^2$. The magnitude of velocity after one second is

(1) 8 m/s

(2) $\sqrt{15}$ m/s

(3) $\sqrt{17}$ m/s

(4) $\sqrt{27}$ m/s

A particle is moving on a circular path of radius \(R.\) When the particle moves from point \(A\) to \(B\) (angle \( \theta\)), the ratio of the distance to that of the magnitude of the displacement will be:

         
1. \(\dfrac{\theta}{\sin\frac{\theta}{2}}\)
2. \(\dfrac{\theta}{2\sin\frac{\theta}{2}}\)
3. \(\dfrac{\theta}{2\cos\frac{\theta}{2}}\)
4. \(\dfrac{\theta}{\cos\frac{\theta}{2}}\)