The gravity in space is given by \(\vec g=-10 \hat j\ \text{m/s}^{2}\). Two particles are simultaneously projected with velocity \(\vec u_1=10\ \text{m/s} \hat i+10\ \text{m/s} \hat j\) and \(\vec u_2=20\ \text{m/s} \hat i+10\ \text{m/s} \hat j\). Then, the ratio of their times of flight is:

1. \(1:1\)

2. \(1:2\)

3. \(2:1\)

4. None of the above

A train is moving towards the east and a car is along the north at the same speed. The observed direction of the car to the passenger on the train is:

Two racing cars of masses \(m_1\) and \(m_2\) are moving in circles of radii \(r_1\) and \(r_2\) respectively. Their speeds are such that each makes a complete circle in the same duration of time \(t\). The ratio of the angular speed of the first to the second car is:

A particle \(P\) is moving in a circle of radius \(a\) with a uniform speed \(v\). \(C\) is the centre of the circle and \(AB\) is a diameter. When passing through \(B\) the angular velocity of \(P\) about \(A\) and \(C\) are in the ratio:

1. \(1 : 1\)

2. \( 1 : 2\)

3. \(2 : 1\)

4. \(4 : 1\)

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is 

1. R/r

2. r/R

3. R²/r²

4. r²/R²

An electric fan has blades of length \(30\ \text{cm}\) as measured from the axis of rotation. If the fan is rotating at \(1200\ \text{r.p.m}\), the acceleration of a point on the tip of the blade is about:

1. \(1600\ \text{m/s}^2\)

2.  \(4740\ \text{m/s}^2\)

3. \(2370\ \text{m/s}^2\)

4. \(5055\ \text{m/s}^2\)

A particle moves with constant speed \(v\) along a circular path of radius \(r\) and completes the circle in time \(T\). The acceleration of the particle is:
1. \(2\pi v / T\)
2. \(2\pi r / T\)
3. \(2\pi r^2 / T\)
4. \(2\pi v^2 / T\)

If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if:
1. a_r = 0 and a_t = 0
2. a_r = 0 but a_t \(\neq\) 0
3. a_r \(\neq\) 0 but a_t = 0
4. a_r \(\neq\) 0 and a_t \(\neq\) 0$\mathrm{}$
 

The figure shows a body of mass \(m\) moving with a uniform speed \(v\) along a circle of radius \(r\). The change in velocity in going from \(A\) to \(B\) is:

1. \(v\sqrt2\) $$

2. \(\dfrac v{\sqrt2}\)

3.  \(v\)

4. zero

An aeroplane is flying horizontally with a velocity \( u = 600\ \text{km/h}\) at a height of \(1960\ \text{m}\). When it is vertically at a point \(A\) on the ground, a bomb is released from it. The bomb strikes the ground at point \(B\). The distance \(AB\) is:

1. \(1200\ \text{m}\)

2. \(0.33\ \text{km}\)

3. \(3.33\ \text{km}\)

4.  \(33\ \text{km}\)